Hi
Pigs love woods but yes, you will need to fence smaller areas for them or you will lose them. Fencing wooded areas can be a bit problematic but possible. They will also need shelter and young pigs need to learn where that is and how to find their way around before they go too far away to find their way back.
Foraging pigs will still need pig food of some kind, whether that is ready made pig ration or you mix or own. They will of course supplement that ration by foraging. As Steph Hen has said soya free will cost more. Mixing your own means storage and mixing facilities for the raw ingredients.
As Steph Hen says know what you want to do with them before you start. I tell new pig keepers to work backwards from the end product because one pig is a lot of meat. Being faced with several finished pigs and no idea what to do with them is not a good scenario. Making money out of pigs isn't an easy game.
Feeding time is also a useful opportunity to check your pigs over and for them to get used to you. Catching, penning and loading "wild" pigs would not be an easy task.
We are assuming you want to finish some pigs and there is no reason why you can't do that slowly and I suggest you don't go for faster growing, modern breeds.