My daughter is 5 and is really sensitive to temperature. She refuses to wear a jumper most of the time, she has only just started being able to tolerate socks on her feet and she gets hot incredibly quickly.
At night I sleep in thermals and have 2 quilts. She gets so hot in her undies, boxer shorts and singlet with 1 summer quilt and blanket that she has to strip off. Same bedroom....
I make sure I take a jumper and socks with us, but I leave it up to her when she wants to wear them. She is happy to put them on when she genuinely needs them and she will ask for them. My little one who is now 2.5 generally is happy to wear jumpers, hats, socks etc. When she was little though I had buckleys chance of being able to keep socks or shoes on her.
The kids also usually go outside to play in the cold rugged up and within about 3 mins they are naked. Its not a problem. They come inside after, have a warm bath and a hot honey milk in front of the fire.
I agree with you if the kids are small enough they can't do anything about it, older ones though - they may have a genuine reason for it. smile