Depends on where the dead wood is. In alpine regions, the Forest Service and Park Service want you to leave it strictly alone. That's because those thin soils need all the decaying organic matter they can get. Fires are generally prohibited at or above timberline for that reason.

Of course lower down in the thick forest, there's plenty of wood to play with!

In the interest of Leave No Trace and the next folks to come along, you might want to toss your shavings in the bushes, if you don't use them in your wood stove or campfire.