Tested this awhile back-- LMOE stoves are safe for 1 piece of splintered wood-- didn’t test larger quantities. just make sure there’s nothing flammable next to them and IIRC you get a medium-sized fire that lasts a bit longer than normal and not a small one. Smoke is a non-issue, just don’t stand right next to it and you should be fine.
Ovens in any house aren’t though. I assume this is because they’re the gas-type ovens you usually have at home. You could light a fire in them reasonably safely, but I think the game considers that you’re trying to light the oven ON fire-- and hey, if there’s any gas left over in the pipes…
Not entered a cabin yet but apparently cabin fireplaces or stoves can be used safely as well, but again make sure there’s nothing flammable nearby-- and if it lights up the floor, well, I havent visited a cabin yet.