We did the Jeep tour in Cozumel last March and had a great time! The Jeeps (and not all of them are "Jeeps"), are sticks. They are open air but I believe there was a fabric top that could be put up if the sun got to much for you. There was a caravan of about 20 Jeeps led by guides to an out of the way beach area. It's off-road most of the time except getting to and from the beach. The Jeeps will hold 4 people. It can be a rough ride on a very bumpy, dusty, sandy, rocky road. We loved it!!! We laughed and laughed until we couldn't help ourselves. We would do it again in a minute. Just keep in mind that it can be a rough ride in sections of the road and you will get somewhat dirty!!!! The tour stops at a beautiful beach for a Mexican lunch. They have volleyball set up on the beach and umbrellas and blankets and you can swim. I think we spent about 1 hour there. The guides were great and very nice and had a nice sense of humor. After the beach stop you turn around and make your way back to the "real" road and head back to town. After parking your Jeep it is only a short walk back to the pier. The guides will expect tips and we didn't mind giving it to them as they were great guys. If you intend to swim, wear you suit under your clothes. Don't wear anything real nice because as I said, you will get dirty. They do provide drinks (bottled water, sodas etc., that you can take along in the Jeep.
By the way, we were on the Sea Princess.
If I can answer any other questions please feel free to email me.