I haven't seen them close the forest to hunting but I have seen them close them to access. Usually when a fire goes through a area you have a lot of burnt trees around the roads and they are afraid that the trees will come down on them, not to mention erosion and rutted roads if it does storm. But even then they will allow hikers into the area, just no vehicles.
On closing down the forest to ATV's, most areas already do that. You have to stay on the roads and approved trails and not just head off cross country.