Ultimately it will be up to you to weigh the risks and benefits and determine whether the risk is one you're willing to take, and to do the research to make sure you're being as safe as possible.
1. Follow the stove manufacturer's directions.
2 Don't use an old antique wood stove.
3. Don't use a tent stove.
4. Make sure your RV has functional smoke and CO2 detectors and a fire extinguisher.
If wood is your only heat source, you're going to need to do some extra preparation to make sure your plumbing and fresh water system warm so that it doesn't freeze.