Wood stoves installed in a vehicle for nomadic living make tons of fantastic dry heat, and they look great in a skoolie or other large vehicle. However, they have significant downsides: they take a ton of space that can't be used for anything else, require maintenance, require sourcing of wood or other fuel, and make it very obvious that someone is living in the vehicle (zero stealth). If you have a very large vehicle, have regular access to firewood or similar combustibles, and the space and maintenance tradeoffs are worth it for you, it's worth considering. Especially if you spend a lot of time boondocking in the remote woods, it might be great.
Some nomads who have installed wood stoves have later ended up removing them, so do lots of research before committing to the idea. Also, a stove probably won't work as your only source of heat, since you won't always be able to use it when needed. See other options for keeping warm. A wood stove can help you get rid of some of the trash you generate. Items like paper plates, cardboard packaging, etc., can be burned. Follow manufacturer guidelines.
Wood stove safety
Wood stoves obviously generate a lot of heat. As such, they can be a fire hazard. Be sure to follow manufacturer guidelines on clearance around your stove, install heat protection on adjacent walls, etc. Be sure that the chimney is installed correctly to minimize dangerous gases inside your living space. Have a functioning fire extinguisher, smoke detector, and carbon monoxide detector in your vehicle at all times.
Insurance
Note that most insurers will probably not want to insure you if you have a wood stove in your vehicle. It is not something they typically deal with (even specialty insurance carriers) so they will probably drop your coverage as soon as they hear about it, and may refuse to pay a claim if they don't already know about it.
Chimney
Generally, the chimney will need to be removed before driving. This can delay your departure in case of emergency, since you aren't ready to leave. See safety and security.
The chimney should point upward to the sky with a cover over it to prevent rain ingress; if your chimney exit is horizontal, you will likely get backdrafts.[1] The top of the chimney should be about 2 feet above your vehicle roof.[2]
Air intake
Your stove needs to draw fresh air in from outside your vehicle, not from inside your vehicle.[3]
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