Winter isn't bad in southern Texas but not warm and toasty...they do get cold spells and sometimes ice. If indeed military parks (we've stayed at several) only let you stay 30 days then you should move around once per month. That can be a plus.
In fact if you can into military parks...head for Key West to Trumbo or Sigsbee. Sigsbee has full hook-ups however there is a waiting list to get in and you cannot stay longterm. Trumbo is dry camping but they have a nice shower house, dump station and you are parked 15' from the water with great breezes. At the time we were there they had no length of time visit at Trumbo like they do Sigsbee so some folks didn't even go on the list for Sigsbee...they just dry camped and were happy. There is a clean laundry facility at Sigsbee.
We also like Fort Huachuca in Arizona.