Agreed with everyone else. It doesn't take long at all to make yourself little paths in the deep snow. We have several "circles" in the front yard and paddock tamped down, as well as figure eights.
It's actually REALLY handy, because it's fantastic for really schooling a horse on leg and seat - they want like heck to stay on the tracks, and you can really feel your work progress as you try using just leg and seat to move them OFF the track.
We've never let the snow stop us. You can't do as much, but you can certainly keep your horse in half decent shape both mentally and physically throughout the winter, even without rings and arenas!