Is it possible to call campgrounds as we go?

We generally travel in the spring before school is out or in the fall when school is back in session. We usually call in the afternoon when we figure out where we going to be stopping that night. Because of our size we usually stay in private campgrounds, so we've never had any issues finding a place to stay.

If we traveled when everyone else does we would probably do things a bit differently, but that's why we go when we do.