I use a tree stand often and yes I get cold. I've started carrying my heavy stuff with me and adding it as the day goes along. I put my coveralls on before I climb up but I don't zip the legs down right away.
Don't get me wrong I use blinds to but the area I hunt here is crazy thick so just being up high gives a little advantage
I've thought about falling as well and I started wearing a knife on my belt in case I had to cut myself free. I used to keep all my little essentials in my back pack but thought if I fall and the bag is the tree it's no good to me