Surely there are plenty of winter hats that don't have any kind of under chin fastening that stay on?? I have 4 under 3 at the moment and only one has a hat that fastens under the chin and none of their hats fall off. If she is wearing a coat then put the hood up too to further secure the hat. Why not make a fun experience out of it and go to walmart or target and try lots on in front of a changing room mirror and see what she likes. Other than that, while I get the sensory issue, and obviously I don't know how these incidents really play out, but I'd be really careful not to feed into this by reacting minimally to her meltdowns. Sometimes a genuine issue can be made bigger with reinforcement even if us as parents are not intending too or aren't aware of it.

Maybe there should also be a period of withdrawl from dresses all together. I know all children are different and it is so hard for me to comment on this not knowing you or your daughter, but I'd be inclined to try and deal with this head on by eliminating the sources of anxiety which to me are the choices she has. If there is no dress to be worn then there is no choice and perhaps minimizing or eliminating the dresses and gradually building up to being in snugly outerwear will just mean a rough go of it until she starts to become desensitized to these uncomfortable feelings. Kind of like an exposure therapy. How about introducing a sensory basket/tub into your daycare full of hats and gloves. That's what I have every year doubling as a dramatic play opportunity and sensory activity. Maybe even make sensory activities a daily thing in your group in the hopes of desensitizing her.

Not sure what else to suggest. I understand some children go through this and it's not bad behaviour, but some things they just have to get used to even if it means daily tantrums. They will eventually get used to things. In the real world outside of the family home without you there she is going to have to deal with it, so best to try and nip it in the bud now rather than have this become a bigger issue for the both of you. It's hard but I'm sure she will get there. Good luck!