Readers won't let go:
I couldn't believe my eyes when I saw your post. My grandparents were from San Marcos, which is about halfway between San Antonio and Austin, and my family went to Aquarena Springs several times when I was a kid. The pig on the postcard is the famous "Ralph the Swimming Pig". Ralph really swam, and he did a water show several times a day accompanied by - no kidding - underwater mermaids. (They breathed from scuba hoses under the surface. It's kind of hard to explain.) Ralph was most famous for his so-called "swine dive," which is what is pictured on the postcard.
My brother and I observed that Ralph was actually Ralphette (the protuberant nipples gave it away).
In my experience with pigs, protuberant nipples are not always a dead cert for being female. Boing Boing a few years ago covered the bulldozing of the park:
Aquarena was the home of the infamous Ralph the Swimming Pig, and his keeper Glurpo, a one-time "nightmarish aquatic clown" turned "underwater witch doctor." There were also "aquamaids" who picnicked & performed ballet underwater, diving ducks, and a sadistic swan named Rufus.