$2000-3500, small truck

You say you're getting this for the winter; I'm assuming you're somewhere where there is snow? If so, a 2-3.5k truck is one of the more dangerous bad-weather vehicles you can buy; they have very little weight in the back end, so you end up spinning out more often than in something that has more even weight distribution. Sure, the 4wd will get you anywhere, but the ability to "accelerate" can mask a propensity to "crash" and to "roll over". And at your budget, you're going to forego electronic stability control which would otherwise help keep you in a straight line. I'm personally a fan of front wheel drive vehicles with snow tires; if you live on a hill or something that front wheel drive and snow tires struggles to get up, then move up to something AWD. Get an old Outback, or something like that.

That's not to say that you can't get a truck, especially if you regularly need a truck bed to haul stuff around in, though. Just be careful and don't count on it to be a "safe" vehicle. As far as brands and models, I'm not sure there's really much advice to give you other than to get one that's been reasonable well taken care of. Sometimes the Mazda trucks can present a good value since folks seem to be put off by the name, even though they're pretty much just Fords. And obviously, if you go small (Ranger, Colorado, Tacoma) you can get a newer/more reliable/better gas milage truck that still falls in your budget.

A few years ago I picked up a clean (not rusty) 2003 Nissan Frontier, 6cyl, 4x4 with 173,000 miles on it. I paid $2,300 for the truck and have also paid $1,500 getting it fixed up ($600 was just for tires). It was a risk but it has paid off! The truck now has 218,000 miles on it, just passed inspection and is still running fine.
Trucks like this are still out there and many are under $4000. They are worth a look.
Negative--- The gas milage is 16 at best.