Yes. Clay is really tough. I have clay with absolutely no rocks at all. I have a sacrifice pasture about 1.5 acres total that gets nearly destroyed this time of year. I also have a small dry lot and an arena, so I could keep them off it, but it would be hard.
I have 3 other acres that I have closed off from now until probably June. It will grow enough grass to make them fat, and keep them busy until the fall and then it will get wet and muddy again so it gets closed until the ground freezes.