Heya... my recommendations for tires:
BF Goodrich K02s
GoodYear Wrangler Duratrac (basically GY's competitor to the vaunted K02s)
Falken Wildpeak A/T3W
All three are proper all-terrain tires (which means they not only look beefy, but they're built to drive over gnarly stuff), but all three also have the snowflake-mountain symbol rating them for winter use, as well.
The Falkens are likely to be notably more affordable than the other two, but deals are frequently seen on any of them. I've driven machines off road with each of those tires and they all handle a multitude of conditions very well.
A/T tires will be more durable and good all-year round, but I would be surprised if your mileage didn't suffer somewhat. You may also notice they're noisier at speed, and at slow speed on pavement, you may also feel the knobs through the steering wheel. (Think about how you can feel a knobbier tire on pavement through the handlebars of a bike, and it's the same sort of thing).
As someone else recommended above, do not go for M/Ts (Mud Terrain tires).