It is absolutely 100% prohibited by written regulations on Federal lands such as the National Forest, the Bureau of Land Management, all National Parks and I am fairly sure all the State Public lands as well to do Oil changes or any other vehicle work which involves chemicals or other fluids including brake work, antifreeze, etc. So get that idea right out of your head. You know how to read and look at websites. Go to the BLM and NFS websites and start reading through the rules and regulations. It is YOUR personal responsibility to do that. No one here in this forum should need to have to educate you on the rules of behavior for camping or visiting federal, state, county or city properties. Those regulations are already written out for you by the agencies. If you are in doubt what they mean pick up the phone and call them!
Now you have your “homework assignment”. Get busy and go to those websites and start reading.