Blazingpedals has the right of it. My biggest problem with my trike on unpaved or in snow is the clearance of my rear derailleur. If the mud or snow is too deep, I end up scooping mud and gritting the chain. Snow collects and freezes the chain solid. Also, rutted ice is doom to a derailleur. I've busted one thanks to that.

Otherwise, the trike is great. Loose soil or gravel is fine. I've taken some fairly rock and root filled trails with just a bit of care to make sure that I pass with the rock or root on the left side. Smooth ice or just a small bit of snow, slap on a set nobby or studded tires and it's good.

One solution to that might be a tadpole with a 26" rear wheel. I've debated converting mine, but it would make it a bit too difficult to get in and out of the apartment.