From what I have read in the DFW Q&A, it is LEGAL to pick up Deer Skulls with antlers attached EXCEPT in local regional parks where you can NOT even take shed antlers. Also, EXCEPT for Big Horn sheep skulls (horns) and Elk Skulls with antlers attached are NOT legal to collect. During hunting season, it still is legal to collect deer skulls with antlers but you will have some explaining to do. Make sure there are no fresh flesh or skin on it. Those are the red flags.
Search "collecting antlers" in their Q&A. There is no provision prohibiting collecting of skulls with antlers attached (Except Big Horn Sheep). I believe Elk is allowed. Collecting is prohibited in wildlife refuges, local parks. Public and private land, OK. This post/question was from 2012. So it may have changed now.