THUMPY

Ava is not very tolerant to the cold. She refuses to wear a coat. She refuses to wear leggings because they're too tight. She won't wear a shirt if the sleeves touch her hands. If you fold them up, they have to be the exact same length. She will not wear socks because they're thumpy. Yes, thumpy is a word in this house. 
On a recent trip to the store to buy some warmer clothes, she picked out some things and told me that she loved them and that she would wear them. We got home, tried her new clothes on and then threw a fit because there was something wrong with everything. I headed back to the store and returned almost all of it. 
So. Here's my problem. We can't avoid the outdoors. If she goes outside, she freezes and I look like a horrible mother for not dressing my child in weather appropriate clothing. Do I let her freeze? Do I force her to wear things she's going to throw a fit over every time she puts them on? Do I search high and low for things that she will wear? 
On the bright side, she will wear a hat. She likes hats.