Speaking of tires...
That is your biggest ally offroad. Having the right tires makes all the difference in the world. A shitty truck with good tires is gonna make it past a good truck with shitty tires 95% of the time. Keep that in mind when picking your truck out.
Tires, knowing how to drive, knowing the capabilities and limits of your vehicle, and most importantly don't be trying to show off cuz oftentimes that results in vehicle damage or getting stuck, seen it many times LOL.
Tires don't necessarily mean you will get through what you are going through, already proved that with my Toyota Tundra with Michelin Street tires and 1-1/2 feet of mud towing an ATV trailer loaded down with camping gear and a Yamaha Rhino down a trail a couple years ago. Those tires sucked, I still managed to get through that trail in 4WD of course without any issues, but I've been driving offroad for many years in 2WD trucks I didn't have the luxury of owning a 4WD until about 6 years ago so I got so used to driving in 2WD I still don't use 4WD very much.
Don't buy tires because they are mud rated either, unless you drive through mud every day they're useless otherwise. Contrary to what people think mud tires do not work very well in snow/ice. I try to just buy all season tires as they seem to work just fine for me overall even in mud, just try and get a good set that are at least 6 ply or you'll have constant flat tire problems.
I was talking to a lady today who owns a 1986 Ford Bronco 2 who lives about 12 miles out of town on a gravel/dirt road. She's owned her bronco 2 since new, and has driven that 12+ miles every day since and she says even in a couple feet of snow she has never had a problem or even thought she would get stuck. These Bronco 2's are extremely capable as long as you know what you are doing just like any other vehicle.
This past winter I drove my Bronco 2 around town a bit in snow/ice, and even with the pretty close to bald tires that are on it, I had no trouble getting around, I did use the 4WD a few times on side streets where the roads hadn't been plowed, but probably wouldn't have needed to, I mainly did it because I was testing everything to make sure stuff worked.
The only thing I really like about the jeeps is they have a large aftermarket for parts, and the Selec-Trac Transfer cases from the 80's and early 90's were great for all weather conditions they gave you 2WD, 4WD high range full time, 4WD high range part time, Neutral for towing with all 4 wheels on the ground, and low range most of which were 2.72:1 ratio. I also got low 20's for fuel economy with my Grand Cherokee and my Cherokee. Something I haven't been able to really get an accurate reading yet on my Bronco 2 as I don't get to drive out of town, and with the current tires on it I won't leave town with it anymore.
Personally for ease of maintenance I'd take the Bronco 2, for aftermarket parts availability I'd take a Jeep Cherokee or Wrangler. I really wish that there was a better aftermarket for the Bronco 2, as I bet it would catch on really quick with offroaders given all of the manual options the Bronco 2's had over the electronic/vacuum assist on some of the Jeeps.
I've had 2 Jeeps and really liked them, and both I had over 230,000 miles on original drive train and never had any major problems other than normal maintenance and wear items. Did a lot of towing with both and was extremely pleased with the power and handling.
I have had 1 Bronco 2 and a Ford Ranger both being 1984 model years. Bronco 2 is 4WD of course the Ranger was a 2WD. I took the ranger many many places offroad following 4WD's every year hunting. The Ranger towed a 16' travel trailer all over the country for 10 years and never had a mechanical problem, just routine services. My bronco 2 I'm not too sure about yet as I haven't been able to get descent tires put on it and have the camber problem in the front end corrected to be able to drive it too far. Kind of leary about going too far with it with the oil leaks it currently has as well. Hopefully this fall I'll get the oil leaks fixed, and here in the next month or so new tires and the camber/alignment issue taken care of then I'll drive it for longer periods out of town. My only huge complaint about my Bronco 2 right now other than the body damage/rust issues is the lack of A/C with the 100+ temps the past month and a half, where I work I'm in 100+ temps all afternoon cooking then I come home to the same it would just be nice to have working A/C but the B2 gets me from point A to point B so that's good enough for me.
Personally if I were in your shoes trying to decide on something offroad capable in stock form without breaking the bank would be the Bronco 2. The Jeep just because of the JEEP name is gonna cost you more plus parts are more expensive as well because most parts stores see the name Jeep and associate it with being a Toy of some sort so the price goes up on parts.