When I was sitting up at night for pigs in Germany, I had (still have) a quilted over-boot. They are impossible to walk in, but I put them on at the foot of the ladder and was able to climb the ladder ok. I too have cold feet. I sleep without even a T-shirt at night, but my feet are freezing unless I wear socks in bed. With those over boots on, my feet did not get the least bit cold. I also have a heavy wool "Ansitzsack" which is pretty much like a sleeping bag in back, but cut only chest high in front with suspenders. NOTHING got cold while wearing that. It traps all your body heat. It has a zipper that runs down one side and across the bottom. I put it on with the zipper unzipped across the bottom and part way up the side. I could climb up into the stand and then zip the bottom up. Fell asleep many times sitting in that.
Of course all this was done sitting in a very roomy tree stand, built from timber and permanent. I'm not sure either would be functional for a "postage stamp" sized hang on, or climber.