Mastercraft Courser CT is great hybrid tire, but not the best for snow or ice.
Duratrac is a great hybrid tire. Good on snow and ice.
General Grabber AT2 (new, more aggressive version) is a great hybrid tire. Great on snow and ice.
Cooper ST (not STT or ST Maxx). If will be used on snow-ice, add extra sipes to center treads. Great hybrid tire.
All those are good on road, and great off road.
Any of those would be a good choice, preferably in load C. At most in load D.
Don't get load E, unless you don't mind a very rough ride.
All those have tough sidewalls in load C, and super tough in D.
C will ride the best.
Warning: I often edit my posts a few times to get them complete, or to correct errors.