May I suggest the Ocala National Forest
North & South sections of the Florida trail
While not particularly
remote from people, it should be beautiful in March. Averages in the high seventies during the day, low fifties at night. The records stand in the upper nineties and mid-twenties, though, so it may be worth paying attention to the weather report before leaving.
In addition, the forest itself has a lot to offer; there's everything from kayaking runs to a shooting range tucked in there. It's worth looking over, even if you don't decide to do the trail.
If you want any information about the Ocala South section of the trail, I can help; I did it this past summer.