You don’t mention what kind of a motorhome, and it’s important to your question.
For motorhomes, “wood” is a highly questionable term. In most entry to mid-level coaches darn near everything is “paper-wrapped” wood product. Meaning, it is very low quality lumber, either solid or ply, that has been shaped and then covered with adhesive-backed paper printed with a pretty convincing wood grain pattern. Refinishing is not an option, but you might be able to paint it, emphasis on the “might”.
As you move up the quality/cost ladder cabinet door and drawer fronts will start to be solid hardwood with traditional finishes, but face frames and panels will still be matching paper wrapped. So, in these coaches you could refinish some parts, but probably not others. You’ll find this configuration even in top-end gassers and some diesel pushers.
And finally, in top-end coaches (one gasser brand that I know of) you’ll get real wood throughout. Refinishing with traditional products shouldn’t be an issue. A lot of work though. There are spray toners that work well for this kind of thing, but you probably won’t find them at Home Depot. Go to a woodworking store (Woodcraft, Rockler, etc), or you might find them in a good paint store.
The paper wrapped stuff is a pain. I had it in my last coach. It can’t be repaired easily, and it’s slick. I can’t imagine that opaque stains or paint will stick, but the only way to know would be to try. In our new Tiffin everything is real wood, and fortunately, we quite like it.
Let us know what you’re driving and we can give you a better idea what your options might be.
2016 Tiffin Allegro Open Road 32SA
2017 Jeep Wrangler JKU