When wilderness camping sometimes you need to pack in your own
firewood. In those instances it may be better to use a backpacking
stove. Most private campgrounds and many state and federal
campgrounds will sell bundles of firewood. One problem with
gathering firewood in a campground is that the trees usually take a
beating. People will cut down live trees and do a lot of damage.
It's best to bring your own or purchase some at the campground. I
recently traveled out west (I think it was in South Dakota) and
found that some states will not allow you to bring in wood from
other states because of the risk of spreading disease to that area.
Check local laws before bringing it with you.