From what I have seen and heard about the Sumpter Valley's Heisler, they burn pine slabs and cutoffs from local sawmills. I don't know how much they consume in a trip. The Climax at the Puffing Billy Railway in Australia also burns wood, but they use eucalyptus, which they refer to as "atomic wood." It apparently has a lot of residual oils in it so it burns very hot. Even so, they have been known to run out of wood before completing a trip.
It would not just be a a change of fuel, either. The netting in the firebox would need to be changed, some sort of balloon stack with additional screening would be necessary, and a whole new method of firing developed. Referring again to the Puffing Billy Climax, they have learned to stuff as much wood into the firebox as possible, leaving the logs long so they almost hit the flue sheet, and keep stuffing the wood in as it burns down. As Gordon notes above, there probably isn't enough space on top of No. 10's tender to carry enough fuel. I've seen photos of woodburners with the wood stacked higher than the cab roof!