you can run hose through snow and work, as long as it is safe to drive etc and don't leave poles out in the cold when its below 0.
sorry stu but your hose will freeze up when lying in the snow, I know i tried it last year, water was coming out back off van but when hose was connected and rolled out it froze before i could get pole on.
last year it was -6 at lunch time where i was and everything froze, but if the outside temp is say around 0 or +1 it will work fine in the snow, the snow is irrelevant, it is more to do with how cold it is. I have worked in around -2 in the snow and if you work fast and don't leave the brush lying around you can work on, although just a chat with a custy can cost you frozen jets.
there is around 8 inches of snow in my garden that my garden hose goes through to fill my van and as long as I able to turn the tap on to fill my van nothing freezes. If however it is say -9 I doubt anything would work. remember it only tends to snow in this country when the temps are 0 or above. not always though