In early February this year, we called and got a small site at Anastasia on very short notice. But it was indeed quite cold with heavy rain all night... kind of a mess since the thick trees overhead dripped for a long time on us, the dog, and the RV after the rain stopped. Lots of tracking in of wet sand.
And like most Florida state parks, the bathrooms/shower houses have open spaces with screening for ventilation across the top of the walls, with no heat of course, and were REALLY cold.
So I'm skipping it for next year's winter route south. I, too, checked on Sebastian Inlet today for next year, and found nothing for late January 2016. But I'm not surprised - it is really popular with fishing folks.
One option you might check is Long Point Park, a Brevard County park with a campground on Melbourne Beach, set on a little island in the Indian River, just north of Sebastian Inlet. Grass sites and not particularly fancy, but in a good location. They now have online reservations.