We've just come back from lapland. It was amazing but so cold (although we did manage to be there during a particularly cold snap). We wore jeans, long sleeve tops and had a jumper in our hand luggage. That with hats, gloves and winter coats were fine for getting off the plane and onto the bus etc.
The big suits they give you are amazing. We wore thermals, then joggers, long sleeve top, jumper and then the snow suit. They gave us boots, wool socks and mittens as well so we all had a pair of thermal socks and normal gloves on underneath. We bought boxes of disposable hand and foot warmers from decathlon and they made a massive difference, worth every penny. I also got a merino wool balaclava from h&m for the kids which were great. We all had fleece neck gaiters as well. I wish I had bought spares as they can get a bit wet when they are over your mouth so it would have been good to be able to change them when out and about. Head torches for tobogganing in the dark would have been useful as well!
Other things that I'm really glad I had with me were a power bank - my phone battery went from 40% to zero after having my phone out for a couple of minutes to take a video. It was fine taking it in and out for a quick photo but it definitely couldn't cope with a longer stint! I also got some water proof phone holders on a lanyard off Amazon. My husband thought it was overkill until he ended up with condensation all over his phone after the first day! I took things like sachets of hot chocolate with us which was nice for the kids to have in the hotel room, and we got a massive bottle of Bailey's from the duty free in the way over. Alcohol is really expensive, although we did try a Lappish beer which was really nice.
We had a meal a short walk from our hotel and just wore thermals and jeans with our coats to get there and it was absolutely fine. Be aware that all of the hotels etc seem to like to have the heating right up so a brisk walk in the cold can be quite pleasant!
Anyway, have a fabulous time, it is absolutely magical 