I have this argument every fucking day with DS age 5 and I used to with his older brother as well. I used to get enraged (silently, inside!) at strangers asking me if he wasn't cold. Once I actually thrust the coat at one and said "Here you go then, you put it on him because he won't let me!" They offered it to him and he was so surprised that he just put it on which of course made me look like I was making a mountain out of a molehill
I eventually gave up because he is some kind of lizard and is never cold.
He is now a teenager and finally let me buy him a ridiculously expensive and thin Adidas jacket 
The worst part is DS can be standing there shivering and INSISTING he still doesn't want to wear his coat. Or for example today he wore his coat but didn't wear his jumper so he was crying for the whole (2 minute) walk home that his hands are freezing cold - and they were, they were bright red. I have to collect 5 jumpers every Friday because his drawers are empty and he has 5 pristine jumpers on his peg. I actually thought that we had surpassed the coat refusal stage because until last winter he basically would wear all kinds of coats, hats, etc no issue at all (whereas DS1 has forever cast off any layer of warmth, I think he is currently sleeping with his window open) but no, apparently he was just delaying it until he realised that he COULD refuse to wear a coat.
OK frustration aside this is what actually helps.
Often the sleeve of a long sleeved top and/or jumper can get pushed up inside each other, this feels horrible and they can't explain it properly to you but we get him to hold onto his sleeves so that this doesn't happen.
Explaining (at a SEPARATE calm time, not when they or you are raging) about concepts like if you keep your body warm then it warms up your blood which will then flow to your feet, hands, etc and make them warm (because his logic is: My body isn't cold, only my hands are cold. My coat won't cover my hands, therefore it won't help. Totally logical. But wrong because it does actually help if you keep your core warm.)
Trying different coats. Letting them pick the coat - I admit here I'm spoiled for choice because a 10 year gap means you have a lot of friends VERY excited about a new baby so I have a lot of hand me downs. But there are also inexpensive coats to be found in charity shops, supermarkets, H&M and Primark. There are many different styles of coat and I'm sure there will be a hideous one that she finds beautiful. We currently have a Spiderman themed coat which clashes with his hair, and a black, warmer one with little sleeve things with a thumb hole.
Have a rule that she can either wear the coat or carry it herself, but you will not carry it for her. It's annoying enough they often just put it on. NB this may fail if you have a buggy and they point out helpfully that they can just put their coat on the buggy so you don't have to carry it either.
Suggest that they wear it just with the hood attached, or with it not done up, as a compromise.
Make a chart showing different temperatures, agree in advance at which temperature the coat is needed. Ask google/Alexa the weather forecast or check phone before leaving the house, cross-reference with chart (good number practice too).
Let them run just outside the door (or open a window if in a flat) to "test" the temperature and whether they think they need a coat or not (has to happen before the meltdown).
Experiment with extra layers e.g. thermal underwear, tights.
Have certain rules e.g. "If it's snowing, raining or you can see your breath, then you need to wear a coat. Outside of these conditions, it's your choice".
Problem solving (again, when calm) - for example today's freezing hand problem was caused in part by the lack of a jumper, but in part also because he'd done drawings and if he had used the mitten things built into his hat/scarf/glove combo then he would have dropped the drawings, but I couldn't hold them either as I was carrying the 2yo who was screaming and had turned into a plank as he had not been allowed to press a button, which was very unreasonable of me as it was a particularly interesting button. So tomorrow I have promised to bring a bag just in case there are any drawings to be carried.