A nail simply pierces a small hole through the bark and into the dead structural wood within. Admittedly, if you hammer hundreds of nails all round the trunk, it probably will damage it. More damage is caused by loose support bars rather than nails. If wood is allowed movement, it will rub against the tree, exposing living tissue and eventually wearing patches of it away. However, a healthy tree should be able to survive even this - it is similar to a branch being removed.
Bolts are the best of the lot for strength and ease of use.
Always use galvanised bolts. Galvanised nails are a lot better than standard steel because they do not rust. Rusting causes brown staining of wood and will weaken the nail, until one day it suddenly snaps when you put a load on it. There may be a problem if the wood is slightly acidic, like oak, because this corrode the nail. However, it is still a much slower process than steel rusting.