I am from the Austin area in Central Texas, so my experience with snow is somewhat limited. However, I am currently visiting my grandchildren in Michigan’s LP, which has lots of snow on the ground right now.
As I was looking at an empty field filled with new-fallen snow, a question occurred to me. Suppose you are a squad of soldiers operating in the area. You know that there is a contingent of enemy soldiers also in the area looking for you. How could you maneuver in the snow while concealing your movements or operations? I can see ways to conceal how many soldiers are in your unit, but I can’t see how you could make the snow look untouched by footsteps, etc. So, how do soldiers operate effectively in this environment (while also not freezing to death!)?
In Band of Brothers the 101st guys dig fortified foxholes with roofs. Then they stay out on the line as long as they can until they rotate to the rear area for a day or so to warm up and eat then rotate back to the front line, They keep several pair of dry socks (inside their helmets?) and keep their feet and toes dry and moving inside their boots to avoid frostbite. I could stand in the woods when properly dressed in 24 degree temps for 6 hours when I was a teen. Could not do that today
As far as leaving tracks, desert dust, beach sand, or dew aren’t significantly different. Fresh snow might reveal terrain features like fresh excavation or perhaps even underground mines or foxholes, bunkers.