Thanks for the advice. In terms of trail, I'm thinking dirt and gravel - nothing extremely rocky in the places I know of to ride.
It sounds like most of you feel my current setup will handle this fairly well, I'm glad for the input - thank you, everyone. I wouldn't have guessed that, being a newcomer and looking at the tires on sight (the stock ones have a fairly smooth profile) , but I'll experiment with them and see if I really do need anything more aggressive.
Thanks and I look forward to interacting with you more in the future!