Hi snaglpus,
Here go my comments:
People here use those half barrels as barbecues . So we cut the barrels in two pieces - could be done on both sides - the longer one with the barrel laying on the side or with the barrel standing.
I've done so too. Unfortunately, those won't last a year and that is with a fire on weekends only... You might get short with the barrel getting holes from the heat.
The iron gets cooked from the fire and will sort of get thinner and starting with holes and rust.
Another thing the guy doesn't say: How do you remove the ashes. He does let it go off and cool as he is not using it all days - he mentions using a couple times a week.
If you're planning to use it all winter, you may have to choose warmer days to let the furnace go off and remove the ashes.
If you try that system, I would use a water pipe to get the heat more uniformly distributed in the greenhouse.
Because there is no way to go under a certain heat, you need some volume in the greenhouse and put the trees at some distance, or you'll cook the trees.
There are woods that will produce more heat; you should target wood burning slower and producing less heat as it will help with the barrel lifespan.
Good luck !
PS: I hope the children of that guy are not as terrible as mine, or he'll have to run to hospital some times ... Mine for sure would at some point ride or jump the barrel or touch it to be sure that it was really bloody hot... Or would stumble and fall near the barrel... Not really secure as a setup... The barrel should be caged.