" ...a (gasp!) snowbird park..." Nothing wrong with that, we did that, DO that for about 5 years now. NJ to Apache Junction AZ., for instance. Most have dog runs, some have areas just for "pet owners"...near the dog runs or dog parks because, y'know, some dog owners, being uncaring lazy and inconsiderate, simply don't pick up afterwards.
But...snowbird parks, at least the ones we've been to, are just, simply great. Activities and great people. No matter where we are, our dog makes everything worthwhile. Of course, we're "dog people".