I was in the Yucatan in February. Although I didn't go in the water at the Progreso beach, I did at Celestun, which is also on the Gulf coast. The water was fine. The Mexicans generally don't go to the beach in the winter, but for us "gringos" from colder climes it was great!
Progreso tends to be very windy in the winter. If a "norte" (a weather front from the north)comes through, you might have a day or two of cloudy, cooler weather. Otherwise, the weather was sunny and in the 80s.