So far I can't tell that the hogs have hurt my pasture at all. I still have them confined in the quarter-acre corral that was vacated by the cows, and though there is little valuable vegetation there, they don't seem to root. They have worked and re-worked the loose hay, but left the ground alone.
I let the paddocks close to the house get overgrazed last year while we struggled to fix our perimeter fencing. To repair some of the damage there and to improve my burned pasture, I've been broadcasting red clover seed onto any bare spots. The legume will add nitrogen and palatability to the grazing in those pastures, especially for my pigs. I'm hoping some well-managed rotational grazing will fix the rest.