IMO, Jamaica Beach RV Park isn't the same park it was a few years ago. They have expanded to the point of losing all of those things that made them such a pleasurable stay.
It's also a fairly long drive into town and all of the things that it has to offer. The beach is across the road as you noted. There is a new RV park south of Jamaica Beach RV Park which looks very nice. State park is OK for short term, otherwise I would rather be on the beach and closer to town.
RV'ers winter on the Island all of the time. So one persons cold is another persons lovely. You will notice salt damage so be aware.