Dreading team build day but don’t think I can not attend

I would just say “Enjoy yourselves everyone, steam and ice not my thing, see you after’”

Well, that's different. I personally hate team building type activities, although from a company perspective I can understand why they might have some potential value, I've never enjoyed that type of thing.
Got to admit, it does sound like they're trying to do something nice that most of the employees would probably really enjoy, and if someone said to me, here's a sauna for you, it's free, I'd really like that.
But I've also been quite sensitive about my body size in the past as well, (not so much now)

I've gone through a lot of stuff in my life, and I've come to realize that nobody really cares what size you are. They know what size you are they've seen you with their eyes they know you're a size whatever, it really doesn't matter.
Absolutely no one's going to be staring at you and thinking "look at OP, she's so flabby, she's so much fatter than I thought she was in real life, oh she's disgusting, she's hurting my eyes, I so don't respect her anymore"...

They're going to be thinking about themselves, how they look, how they come across, the conversations they're having, and any insecurities they have about themselves ..their body hair, their wobbly bits, their spare tyre...
Most people are absolutely not thinking about you. Most people barely register you as part of their day, they think about themselves.
I am certain that you would be fine, and that if you relaxed you could enjoy yourself (as much as one can on a employee team building activity day)
I agree, have a nice cover up or robe to where until you get right to the sauna part where you take it off, it'll make you feel less self-conscious to have some sort of cover up, aside from that, hey, hate to be a big time downer but you're probably better looking now than you're going to be in 5 or 10 or 15 years and you look back at that time at photos of yourself now and you'll say God I actually looked really good I can't believe I felt that I was fat or unattractive. Look at me now....

Looking back, we always worried more than we needed to.

I have POTS I would faint in a sauna - shame I couldn’t go I’d have loved to.

OP you get migraines right and it triggers them? 😬

Rush to the toilet in the office that morning like you're feeling unwell, then tell your team you're really sorry, but you've just been sick. go home.

This sounds like total gaslighting

Work on your confidence!!!

No one is obliged to wear a swimming costume in front of anyone, no one has to feel comfortable with it and if someone does feel comfortable with it they still might not want to.

So what if you're ok to do it, so what if someone isnt ok to do it. We have choices and autonomy in life.

Sadly, I would have some important work to finish that would mean I had to miss it. If I couldn't do that I would have a headache.

I completely agree with @Bucketfulloftears don't make excuses especially as they could be "fixed" but just say you're not comfortable taking part. Perhaps your manager will say something about not acting as part of the team, I'd challenge that and say they need to come up with more inclusive activities.

However, is it really that bad? I'm 60 and size 20, I often travel with team members for workshops etc and we stay in the same hotel and use the pool/sauna together. I have never worried about it. I mean this kindly and gently - can you not work on your confidence? Either so you can take part, or you can speak up at the time of the suggestion and say it's not for you.

God almighty some of these replies, risk assessment, diversity assessment, reporting to HR, blah blah blah

No need for all of this, some mad people might like the day and others, like me, would say, see you the lounge, Im having an aperol spritz thanks. (and get reported for being under the influence!!!)

Do not “forget” your swimwear, someone will find a way to get you a replacement.

There is no way I would take part in this, and I would have no trouble refusing. It’s completely inappropriate to put you in a situation where you feel physically exposed and vulnerable. I’m wondering who has done the diversity assessment on this one, how about people of different faiths, different gender identities etc?

Don’t make yourself ill with worry over it. Just say you won’t be taking part in activities which require you be to unclothed in the company of your work colleagues.

If it's just the swim wear that's a problem, look for a rash vest / t shirt and board shorts or look at 'modest' swim stuff. There's plenty of clothing in a suitable material for getting wet that covers more skin than a typical swimming costume.

-You don't have to forget your costume. What if someone has a spare?
-You don't have to spend money to buy a costume when it's probably for a short part of the day.
-You don't have to give any excuses
-You don't have to remove any clothing to be with your colleagues.
What you need to do OP is simply say sorry not doing that part of the activity day as don't feel comfortable doing it. I bet a few others don't want to do it either.

I’d absolutely fake an illness that day. I couldn’t be arsed to explain my personal reasons for not stripping down to swimwear in front of professional colleagues.

Agree with this comment 100%

I love saunas. Hate team days. Refused to go on an old job’s one. You couldn’t get me into a sauna with colleagues! Don’t ‘forget’ your stuff, there’s going to be someone who’ll suggest going in in your bra and knickers. Just say not for me thanks, see you later. If you want to be snippy or get challenged, say that partial nudity exceeds all reasonable expectations of your role.

I’m pretty certain this would trigger my IBS…

And if it didn’t I would say it had.

I'm confident about my body but the last thing I'd want to do see colleagues in swimwear. Sounds like a fever dream! YANBU. I'd just say openly I'm not comfortable with that activity and will not be joining them for that part. They can't make you do it.

Just say you don't do saunas or ice baths. Be blunt that you cannot tolerate either. Send it in an email to your boss saying that you won't be taking part in those specific activities, but happy to go along to socialize. I wouldn't be weird, cagy or defensive about it. Just say to your colleagues you cannot tolerate extreme temps lime that, it leaves you feeling very ill.
If you do go, maybe take pics, offer towels, join in on fun and laughs to stay part of the group.

Contact HR. There are a few cultures where this would be unthinkable.

Even if you don't have religious Jews and Muslims working there at the moment you might in the future. No woman should be expected to be in a state of undress with males.

This is the best and simplest answer to your problem

I hate team building exercises, they are always bloody awful. Bit like being at school and having to participate in sports day, when you hate sports!! I think a sauna with work colleagues sounds like a nightmare! I wouldn't want to do that either. I'm surprised HR agreed to it to be honest. I don't think it's appropriate to put staff into a position where they may feel vulnerable and/or anxious. I'd either make up an excuse - high blood pressure (or similar) means you can't take part or be honest and say you feel extremely uncomfortable and will be passing on this activity.

My god there are a lot of fannies on this thread, whatever happened to just saying thanks but no thanks?

You're a grown woman not a kid trying to get out of a test at school - don't make up some convoluted excuse, just tell them no, along with all the really valid reasons this is a stupid idea. They can't force you to get your kit off in front of your colleagues.

I wouldn’t want to see any of my colleagues in swimwear, or for them to see me. I cAnt believe you’re alone in your reluctance!

This is such a bad idea I can't believe that your firm is planning to do it!

Absolutely no way in hell, never. No.

I'd tell them you have high blood pressure and cannot participate, so will see them when they have finished.

Absolutely this. Its not big deal, you say no, Im happy to wear my clothes and sit in the cafe, see you after your activities.

Chances are if you are fully clothed theres bits of the sauna you cant go into, thats also fine. Sit in the restaurant or lounge bit, take a book or games on your phone.

Dont make up things like you're ill, forgot your costume or whatever, its not necessary. You're just happy to sit there and dont want to get changed thank you very much, I dont want to wear swimwear or a robe and Im happy sitting here thanks, have a nice time everyone

Speak to your manager. Say you're looking forward to the day and some activities but unfortunately you are not able to participate in anything that involves you or others getting undressed in the workplace.