Possible to cook chestnuts on a wood burning stove?
Chestnuts can be rosted in the oven, no special equipment necessary. You should prepare them properly, though. First, soak them in lukewarm water for at least 30 minutes. This will soften the skin and help to loosen the fuzzy inner skin later. Then, use a small knife to cut either a slit or a cross on the round side. Place them, cut side up, on a baking tray and roast at 180-200 °C / 350-400 °F for about half an hour. The cuts should open when the chestnuts are done.

If you want to try this on your stove, prepare them the same way, then roast in the pan. Aim for a rather hot stove, mimicking the coal fire, stir them often. If possible, use a cast iron pan rather than non-stick, as the coating might suffer.  Some street vendors here add a dash of water to the roasting pan (over the coal fire) to create steam once in a while. As to time: see above, cuts should open and chestnuts can be easily pierced with a knife. 

Did you know than you can also boil chestnuts? Prepare as described above, then boil for about 10 minutes.