Depends on the snow as far as cooling. I find that off-trail in deep, cold snow, it can't keep the temps up to anywhere near operating temp without engine shrouds, unless you're climbing and on the pipe for a while. Snow just packs in around the cylinder when going downhill and you'll see 75 degree coolant temp coming out of the head in no time.
Spring conditions, yea, it will get warm when you're riding it hard and not moving fast enough for radiators.
Carb heat is definitely needed for the cold, deep days. I actually had my carb ice up once this winter after blasting full throttle across a big open area for a while when it was 0 degrees and deep snow. After letting it idle for a bit, the carb warmed back up with my carb heater and it was fine, but scary when it happened at full throttle.