I like a .22 in the winter because most of the time the squirrels will be on the ground and I can take advantage of the extended range of a .22.

Snow shoes

Treestand. How do you weight?..gain it, or lose it? :)
Being funny. I make those mistakes all the time with my English. I would consider where you are hunting. If there were houses say within a half-mile, I would use the shotgun. That .22 can carry a slug about a mile given the shots that would be taken up in a tree.

same as without snow, but you can see their tracks which makes it easier.

4's ?? 7.5, or 8's work best for both squirrels, and grouse. You must wanna hit them in the hindquarters, and break their neck.

I hunt them just like I would if there wasn't snow on the ground. Slow stalk through the woods keeping an I eye on the ground and in the trees. A lot of times you can spot a squirrel warmimg his self in the sun layin on a limb high in the trees so keep a sharp eye out cause they are hard to see sometimes when they are way up there. A 22 is what I like to use cause it shoots farther and if you get a good head shot it doesnt ruin the meat