I'm perhaps beating a played-out thread here, but having recently shopped for a SUV in the 15-20k price range, I figured I'd go ahead and share my experience.
From what I've seen, it will be difficult to find a reliable SUV in that price range that gives you the space you have in the Jeep Cherokee. If you're looking at cars that are a few years old, that price range will be mostly RAV-4s, CR-Vs, Mazda MX-6s, and Subaru Foresters, all of which are likely to feel too small if you're used to a Cherokee. Most of the mid-sized SUVs in that price range have serious reliability issues (Ford, Hyundai, Kia, Chevy Traverse, Nissan Rogue, various Jeeps). If you're willing to go older and higher mileage, you'll have more possibilities, but obviously such vehicles come with maintenance and repair commitments.
After considerable searching, I managed to find a 2010 Toyota Highlander that looked like new, had no rust, and only had 68k miles. But because it was almost 10 years old, it fit within my price range. That was truly a lucky find. I looked at several 4-runners, but the only ones that were even close to my price range had high miles and rust underneath.
I also wanted to share my experience with snow driving. I've spent 16 winters in an area that gets a decent amount of snow, and during that time I've owned and driven front wheel drive sedans, as well as 4 wheel drive pickups and SUVs. In my experience, there is a definite difference in performance. I find that a front wheel drive sedan with good tires does fine in small amounts of snow and ice, and on mostly flat city streets and highways that get plowed and treated. But if you have to drive up steep hills, or through unplowed snow that is more than about 3 inches deep, you run a high risk of getting stuck. Four wheel drive vehicles can handle those situations, unless the snow gets deep enough to drag the underside of the car.