Early May can be quite variable. No direct experience, but even for those private CG's that are open, there may still be quite a bit of snow and certainly mud on the ground.
I'd suggest (as others have) calling ahead. I think the weather will be good enough that you should plan on your trip, just plan each day when you need a spot to stay.
40's - 50's is probably the likely range of temps. Could be bright sunshine or grey crud. A lot of the ground issues depend on the snowfall the winter before and it's been relatively light this year in the SC area...although heavier in spots.