I used to have a 92 Explorer Sport that did just fine on southern Carolina beaches. It was lacking in ground clearance, but I never had a problem with it. I did over heat it once at Fort Fisher, but it was a 100+ degree day and I was young and stupid and ran the AC. No fire, but I learned AC and sand did not mix. No problems after that in the sand or mud. Ran slightly larger tires than stock.
I also had a 2000 Durango that was great in the soft sand as well as deep snow. I loved that truck and wouldn't hesitate to take it through just about anything.
The key is the tires and using the proper pressure. I have a 2013 Jeep Grand Cherokee right now and it's plenty capable, but it has 20" rims, so it's not as good in the sand as my Durango was. It does fine and with the air suspension has more ground clearance, but truth be told I felt better in my Durango. The GC is definitely better on the road and much more "fancy" with the tech.