Haven't hunted with a Suby for a number of years now, but when I owned them it was all I had. Like buffybr they were older ones. My last was an '84 with the 2 speed "transfer case". Went a lot of places in that thing. Never lucky enough to have scored an elk when I owned it, but since I could get 1/3 of a cord of wood in the back (Measured space with seat down) I figured if I had there'd have been plenty of room, especially quartered or boned out. A bulls rack? Well, there was a roof rack for that.
Hunted the Big Boquillas ranch in N AZ a few times. Place on there , ranch house with corrals/cattle pens. One called the "bull pen". Road on the low side of was not a car friendly road. Came down it in the Sub wagon one trip, had to move a boulder or two to the side of the road, nothing major. Coupla guys meet me on their way up, near the bottom. Asked if I came down past the bull pen (as if there was another way??) , in THAT car? I said yep, no problema.
Someone mentioned the ground clearance on them. Bought my first Sub wagon in '77. Advertised as the same ground clearance as stock CJ-5 at the time. Not sure about the newer Forester models, but my brother owns one (2015?) and he runs around FS and ranch roads in N AZ taking pictures all the time.
Maybe try to plan for the earlier season hunts? When roads are likely to be drier. And avoid the Kaibab in the wet.
Oh, get a good mud/snow tire installed too.
Good luck and enjoy your hunting.
Geno