I was wondering this last night! Ours isnt fozen so Im going to give it ago tonight. Ill prob put some vas or some thing in horses feet though, so she doesnt get snow balls!
As my horse (as with all of the rest on the yard) has been kept in these past two days I ventured into our manege last night (others had lunged in there earlier). I led my girl about in hand around the same circle for about 15 minutes. Before I came out of the school (its rubber on sand) I picked her feet out... I would have been better off with an ice pick as she literally had ice and rubber "stilts" in there... I certainly wouldn't want to be aboard when she has all that in her feet
Have been told putting vaseline inside the hooves can prevent it sticking and make the snow "ball" but haven't ever tried.
So in answer, I wouldn't think it safe to ride with feet packed full of snow and ice....
I have been the only one on our yard of 40ish to ride these last 2 days in the school it has snow but doesnt ball up in her feet, she was working great in there. The lunge pen has now frozen and the other school is frozen too, but she has gone out for a few hrs today so at least I get a day off!!!