Ghost, I can only speak for Colorado...
Public or private land no difference...it is PERFECTLY LEGAL to pickup a dead skull with antlers attached.
Now, that being said, if you come strolling out of the woods at any time with a really fresh head that you may have legitimately found dead, your gonna get quizzed by the DOW...you might even be asked to show them the place where you found it and if they think it might have been poached by someone they are gonna take the skull for evidence. You might get it back after the investigation.
SO, again, legal in Colorado to pick up skulls on public and private land.