Here in Utah you can get a permit to cut wood on BLM land. It costs $6 per cord, but you have to get a permit for 2 cords, so $12. They have areas that you can cut standing dead that you can cut year round, but the access is less than optimal during the winter months. There are areas that you can cut live trees as well, but here they are mostly in winter range for wildlife, and only allow it after the spring thaw. Just look up your state and blm wood cutting permit. You'll find out.
I have cut wood from peoples yards, and other private property. Always with permission. You can also call a municipality and ask what they do with wood they cut. The city I work for will give it to people if they want it, otherwise they take it to the landfill and turn it into mulch.
Tree cutting services usually have to pay to dispose of wood, unless they are selling it for firewood, and here that is rare.