Out of all the SUVs you mention, the only one that will likely be reliable is the Lexus. The others are so-so. The Jeep will be cheaper to fix than the German cars, but will likely break down just as often, if not more. You'll also need to go pretty old to get one of these within a $22k budget. Hold off on some money for future repairs with the SUVs that are not the Lexus.
The Lexus will do everything well, except for the "fun" part. It just doesn't handle that well and is meant for long road trips and comfy and quiet cruising. The other SUVs will have a more firm ride, but handle better.
The only other similar car to add is the Acura RDX. It is a little less refined than the Lexus and a little more sporty.
Snow tires with FWD is much more effective than all season tires and AWD at getting through snow. I would get some all-weather tires because they are supposedly good to leave on year-round and are great at everything.
2016 and newer Kia Sorento, Toyota Highlander, Honda Pilot, Subaru Outback, 2016 and newer Mazda CX-9, and 2017 and newer Mazda CX-5 are all good choices.
Note that SUVs are expensive right now as everyone wants one, including the used market.