The Forest Service frowns upon posting any No Trespassing signs anywhere in the National Forests. Any sign you want to place on your cabin needs to be authorized by the local district officer in your Forest.
I have seen one or two signs in or on cabins, but those seem to be overlooked exceptions. Check with your forest and if you have particular concerns, also share those with the agency officers. Increased crime is a concern that sometimes needs to be communicated.