There was a post a ways back on the Surly blog, before they released the LHT, about testing it off-road. They said good things about it (of course they did, they built it!), but remarked that rear wheel slip will happen easily on loose ground or steep hills with loose ground. That's because of the long chainstays. Other than that, it should be fine. You should avoid going over too many logs - the lower BB means you could bash a chainring.

By the way, Surly also makes the smaller sizes of the Cross-Check for 26" wheels, so that's still an option.