With my hammock, I've stayed on the east coast since the weather is pretty predictable, no mountains or other places that could get cold really quickly. For traveling longer distances, I tend to carry a bivy sack, since it's more compact and suitable for colder weather.
As for the big trees, well, the main reason for the webbing is to protect the tree, so if the webbing is too small, then you can just use rope and shield the tree with fallen branches/rags/whatever around the perimeter, so that the rope isn't touching the bark directly.