Seems dangerous and I can't imagine the smoke is good for the trees.
I have a super crazy idea. Please disregard if you think it is too out there.
Actually, I would take that idea and modify it slightly. I would get some potatoes (yes, potatoes) and throw them in a 450 deg oven for 2 hours or so. Potatoes have a huge thermal capacitance (more than most metals) and will release heat over a long time. In fact, my wife's grandmother used to put warm potatoes in the pockets of her children to keep their hands warm on the way to school in the Illinois winters. Obviously not as hot as what I am suggesting here, but the same principle. Puncture so they don't explode.
Then wrap them in several layers of thick Aluminum foil so they don't attract wildlife. Use grilling gloves to withstand the heat while you wrap them. You don't want to wrap first because you need to puncture the taters at that high of heat or they might explode, And if you wrap first you will puncture the foil, which will defeat the purpose of a foil barrier to trap in the aroma.
My yard is small enough that I can get Christmas lights to where I need them. Except for one spot.
For this spot, I am doing a play on this radiant heat idea.
This idea is not so crazy, so you can use this too:
I have large black plastic garbage cans that I am using as compost and verimcompost bins. In winter, I am planning on leaving them in the sun all day. Then at night I am going to wheel them next to my tree that I can't get with C9 lights. The idea is that the absorbed solar heat + the decomposing matter will give a gentle heat all night long (probably 200-300 lbs of decomposing mass). Cover both the tree and 'compost bin' with a frost cloth to trap in the heat.
I know this is early but I'd like to be prepared when the frost/freeze come this winter.
Has anyone tried using charcoal as a source of heat under their trees? I got this idea from someone that said they light some charcoal and place them inside cinder blocks and cap it and placed underneath a tree, the heat lasts for hours. Seems like a good idea, especially for the farther parts of my yard where I can't run any extension cords to but what I'm concerned about is the smoke. Would it suffocate the tree if the tree is covered in frost cloth as well?