So I ran a 2000 extended cab 2wd Ranger for a number of years in all sorts of crazy weather and stuff. Factory all seasons were absolute trash. Had a set of Firestones, I believe that pattern was modified and became the Destination pattern. Garbage. Had a set of Remington tires and they were great, but I think the company is gone. Had a set of Sport King AT tires and they were great, but I think that company may be gone too. Weight was helpful, I think I ended up keeping 200# in it when traction was needed. Ended up swapping to a limited slip and only ran it like that a short time before being young and dumb slid it off the road. Driver error, nothing to do with the vehicle.
My F-150 is 4x4, but had an open rear with generic tires, which sucked. Replaced those with Nexen AT tires which were worse despite having decent looking tread. If it rained, I had to use 4x4, even with about 200# in the bed. They lasted about 8k before being gone. Put a locker in the rear (lockright lunchbox locker), and put Mastercraft Courser C/T tires on. Got 30-40k out of the first set and it would go wherever I pointed it, but when it got really slick out the locker wanted to push me straight so I had to use 4x4 more than planned. I’m on my second set of C/T tires.
My green Ranger had nearly new Hankook AT tires when I got it and they sucked. Dry pavement was somewhat ok, rain or snow and it was useless. Open rear end and even having 4x4 was little help. Replaced them with Mastercraft Courser CXT (they replaced the C/T pattern). Now that truck will go anywhere.
My choptop Bronco II got Gound Hawg knock-offs when I first put it together and they were great. Replaced with BF Goodrich and have mixed feelings, they worked ok but I intend to replace with Mastercraft MXT at this point. It also has a packed limited slip in the rear.
My red 92 Ranger has limited slip and had Kenda mud tires. So far I have been grudgingly surprised with performance.
My parents ran Destinations on their Explorer with meh results. They got replaced with Mastercraft Courser AXT which were an improvement. Their Ranger also got AXT tires and they have been quite happy with them.
I typically run more aggressive tires because my trucks often end up off of paved surfaces. In your situation I think a good AT tire would likely suit your needs. FYI, Mastercraft is Cooper’s off brand with old tread patterns and such.