If you swim in Lake Michigan during summer, you might find that the water off Gulf shore beaches in Jan-Feb is not too cold, if air temperatures are not too cold, and those can vary quite a bit in that season. People's temperature preferences vary, some won't go into water cooler than 80 F, others don't mind splashing around at the edges when it is 60.
My daughters at that age, and my granddaughters now, liked walking the beaches in cool weather, exploring, but also preferred to be dressed so that they could get into the water from time to time. When younger, it was hard keeping them out of it no matter how cool, but as they got older more things interested them. Beaches on Mississppi Bay may be more interesting for exploration, as some beaches right on the Gulf might be too clean to be interesting, even after a storm.
For a couple years my daughter lived two blocks off the beach at Ocean Springs, and were good to go exploring "their" beach anytime it was not cold and wet ( characteristic of winter weather on that coast), but to "go to the beach" for what people do there when it is warm, they preferred a cleaner, wider surf-swept beach.