Our home has been insured since we finished it, 1985. It's always been wood-heated, plus fireplace. No problem.
However, a few yr. back, we had a huge forest fire about forty miles from here, took out many homes, human-caused by a Forest Svc. employee, I think it was. Eventually our agent showed up without notice, inspected the house, luckily I had fire extinguishers all over, near both stoves and otherwise. I pointed out our insulated stovepipe [MetalBestos], steel heat shields behind the stoves, and so on.
He wasn't impressed with anything. Said that the co. [Farmers] was reconsidering mountain home coverage, no doubt due to the hit they took on the big fire. Few weeks later, we got notice of a rate increase and it went up a couple hundred bucks. However, they did not cancel us.
Few months ago, I was shopping for a different auto insurance deal, and several co's I looked at offered a better deal for homeowners, if we added that, too. Usual deal. When they found out we were wood-head and mountain property, only one was willing to talk. And we were rejected by that one because, the agent claimed, they would only insure homes with "central heat." I tried to pin him down on just exactly what systems would be included in central heat, and he couldn't or wouldn't tell me. I asked if it had to do with wood heat, and he refused to tell me that, too. I mean, I asked whether any wood systems would make the "central heating" description. No real answer.
Again, this may have to do with the big fire a few yr. ago and the hit the co's took back then.