What do you mean, wood burning can be green?
In fact, masonry heaters (which are also sometimes called "Finnish heaters" or "Russian heaters") can be a green source for heating a home. While a traditional fireplace may be only 10% efficient (which is to say not!), a masonry heater can be 90% efficient. A well insulated house (even in a cold, Canadian location) can be heated on a single cord of wood per season. In a sense, a masonry heater is to a traditional fireplace what a compact fluorescent (or, even better, and LED light) is to an incandescent bulb.