You mentioned "deep snow". Be careful with this whatever tires you run. Even 2" of snow is like riding through sand. It will slow you way down and tire you out.
I ride 25 miles round trip, and riding home 12 miles in only 2 inches of snow takes me 75% longer and absolutely drains my energy.
Agree. This was my first winter riding outdoors on any kind of regular basis. I found 2-4 inches of snow (depending on moisture content / heaviness of snow) to be my limit - i.e., where it became far too much pain in the anus to be any fun.
In general, I think riding snow
is a lot like riding in sand - slide your butt back to unweight the front wheel, keep your cadence up, etc.