We have Yorkshire (Large White) pigs and they get almost all of their feed from pasture. Some years we have done over 95% of their feed just from the pasture and then hay in the winter. May through November they are out in the fields. They are just now settling in to their winter quarters, our garden corrals, with lots of hay.
I suspect that many breeds will do fine on pasture. The big issue is not getting culls from the big commercial confinement breeders who are aiming for a different kind of genetics.