The traditional story was that the wood was gathered locally by the "forest kommandos."
That is of course not realistic, so more recently Holocaust Controversies has been forced to argue that there must have been enormous undocumented wood deliveries to the camps.
See Mattogno et al response to Holocaust Controversies, starting pg. 1269.
Basically all testimonies speak about Waldkommandos (forest commandos), squads of detainees appointed to the cut down trees in the nearby forests to obtain wood for the cremation, but for Muehlenkamp this holocaustic truth is intolerable. He appeals to only one witness, whose name Arad distorts and whose statements Muehlenkamp interprets according to his own convenience. Werner Becker in fact declared:
I performed various services, as already stated, I brought victuals for the camp as well as wood for the combustion of people.
In this regard Schelvis writes:
The burning of the corpses, at that time already more than one hundred thousand, required a vast quantity of wood, which was abundantly available in the nearby forest. A forest commando was formed which consisted of about 30 working inmates. Under the supervision of several SS members and of Ukrainian security guards it had to cut down trees and saw them into small pieces.
For the mainstream, I would guess the "forest kommando" thing is still the standard story. But details like that are the sort of thing they handwave on. For anti-revisionists (who often come up with their own versions of the stories that are different from the mainstream), I would say they've moved to claiming hypothetical wood deliveries.
With the forest kommando story, the wood would be green unless they gathered a huge amount in say the spring of 1942 and let it season during the summer.