When I used to put them in most of them required we run #12-2 w/ ground.
What we did was ran a 10-2 with ground, put an outlet at the woodburner and installed a ground rod at the unit for an equipment ground. The reason we put an outlet on the outside of the unit with a disconnect (light switch inside the control cabinet) was so that we could hook up a light or other tool if we needed to and be able to kill power to the unit as a whole if we needed to. We figured we may be working on them at night and almost always it would be in the winter when it would be cold and probably with the ground being muddy or snow covered and we wouldn't have to go in the house to kill or energize the circuit.
And since we were an HVAC company we didn't do any underground electric other than these wood boilers and we'd buy a large spool of 10-2 underground wire that would cover anything we ever needed to do, and we usually put them in for farmers notorious for adding on to an existing circuit where a circuit was already ran. Often time the owner would build some sort of structure nearby to house wood under which had lights for working in the dark.