mine run thru the woods and it doesnt seem to get too bad, the more space the better.
the ones that were in a little paddock poached it very badly so we sacrificed our grass paddock and will roll it and reseed it in the spring - it needed doing anyway!
next year we will fence off more woods for them as they prefer to root the grassland than the woodland and quickly turn it to a mess.
we did finish 3 porkers inside once, they had a stable and adjoining yard.
if u dont have spare land to use, then consider the seasons you will be finishing them, maybe avoid winter.
as for the pigs u have now - pray for frost, that stops them sinking so deep...lol