+1 on the full coverage fenders, they help. But if you ride in deep enough snow, you'll pack the rear cassette with snow eventually, which might be what's happening. If the chain is still grabbing the chainrings, then the problem is at the back of the drivetrain, and it's a pretty common one for snow cyclists.

When riding in deep enough snow to be kicked up into the cassette, I just pick a gear and stay there; as long as the chain doesn't change cogs then the cog you're on will stay usable and the chain won't skip.