Trucks would still be used. The horses are only used to drag logs through forest. In the standard industrial logging as we know it, skidders of some sort drag logs. Somehow, either way the log gets from its stump to a truck.
Word is that horses are much lighter than the equipment currently used. Not the same sort of abuse of soil and roots.
Some good reading here:
https://www.treefarmsystem.org/bulletin-bring-some-horsepower-to-your-logging
I'm not looking to "play" logger. I buy lumber all the time. Someone harvested that. My greenie BiL (the other one is a tea partier) believes that healthy forestry and logging (and replanting) sequesters carbon. Good enough. I might be able to make some money in this.
I think draft mules have a future in logging. Horses too, but mules deal with heat better.