I have BFG AT, I think they're 265/17 whatever stock is. I could definitely do some things to make my Silverado a little better but I need something smaller to get around on our 2 tracks.
This is what the run in Iceland, driving on glaciers and snow half the year. Tacomas and SUVS the like are preferred, including defenders, etc. Big tires, aired down. They are riding on top of the snow and not digging down to the dirt. If the depth is low and you'll dig down, then skinny tires are better, more pressure.
Chains are important, if you're going to be on snow the whole time, why not chain up and have the that extra grip. Nobody gets stuck without chains on and says: "glad I didn't have chains on until now"
If you're way up the backroads hound hunting, reliability is important. I'd prefer 4x4 over awd, I don't like the fact that a lot of awd spin the tire with the least amount of grip as they don't have lockers, but modern awd systems are impressive and can do well in a lot of conditions.
The Gen 1 Tacoma is your Huckleberry. I daily drive mine in addition to using it for what you are, and it's ideal. Mechanically reliable (unlike anything that says Jeep on it) and off road oriented. Find the V6, TRD Off Road in a manual. 255-85/16s are the way to go if you don't want to make major mods to accommodate anything bigger (steering, CVs, fiberglass, etc). The Toyo M/T is my favorite. Measures out to 33.5x9 on the treads on stock wheels (which are the best option, only wheel that narrow that I'm aware of). You'll have to trim if you want to run chains at flex, and will only be able to run them in the rear without swapping UCAs. The aftermarket following for them is excellent, you can find just about anything you need change or upgrade.
Another thing to add is that skinny tires are the only way to go, unless you go all the way to a dedicated snow wheeler (like the one pictured above). That means 40"+ tires at least 14 wide. Nothing less than that actually floats. Pushing through crusted snow, sliding on muddy roads for miles... You'll hate the wide tires. Skinny tires have far less forward resistance, steer more easily, have more pressure on their footprint, dig to traction better (we're talking mountains, not swamps), and air down more effectively than wide tires. M/Ts do better breaking through deep snow. A/Ts do better when it's packed, but they don't keep up in deep, unbroken snow.
Tall and skinny are the way to go at less than 2 feet of snow....same with chains, but.... Any tire aired down WILL do better in snow regardless of size even at a foot or less of snow. I have personally been in/on 3 ft with 255/85/16s at 12 psi, many times. Same rig now has 40s, running anywhere from 2-5psi depending on snow conditions. Depending on the year, we will run between 1-2 thousand miles on snow.
I've pushed snow with the bumper coming out of hunting camps many times after heavy snow storms. Here's a pic of just normal snow use. Chained up the fronts just because of a steep grade we had to go up early on, long before getting back here. Hard to go wrong with a Toyota, especially if you chain up all four.
Couple guys mentioned SxS with tracks and we just got into that with ours. Not sure what your definition of “deep” snow is to you but we’re running our General 4 in snow conditions above 2ft and does fantastic. You know as good as i do you can only get so far with chains in deep snow especially if the snow gets crusty
Ya our issue is we don't hunt Backcountry so we go back and forth between paved road, dirt road, two track, field, and whatever else in a matter of minutes chasing. So it really has to be just a pickup. Chains not really an option either with amount of roads we run.
Ive got a 2013 Xterra Pro 4X, comes with the factory locker. I have had it in some scenarios that would have been pretty white knuckle in many other rigs, and the litte Xterra just chugged along fine. Deep snow, thick slick backcountry mud, steep rocky jeep trails, all have been no issue for it. I do like the Tacoma's and 4Runners alot too