San Antonio is not much more than three hours from the Houston city limits. Admiralty RV Park on the west side of San Antonio sounds like your kind of place, my own SA preference was Traveler's World just south of downtown San Antonio, but that's for access to the city center, rather than what is at the RV park.
I've looked at the RV parks in or close to Houston (particularly close to Medical Center) and did not find any that really looked like snowbird resort parks. But then, with frequent but short-lived winter storms, Houston is not really a snowbird area. That would be Corpus Christi, Port Aransas, Rockport, Padre Island, all another 4-5 hours further south. I traveled to Houston 6 to 8 times a year over twenty years, encountered winter weather more often than I expected, usually freezing rain rather than snow.
There are resort areas around Lake Livingston, east of Huntsville, that have large RV parks. There is the town of Riverside on TX-19, and Pointblank and Onalaska on US-190, that have RV parks with many long-term residents, but I know nothing about these facilities and what might be the active seasons. My travel through these areas was year-round, but my destination was Houston Medical Center.