I'm somewhat new to biking, and I've been commuting to work on my new touring/hybrid bike for a few months now (it's a 2014 Novara Safari). I am very interested in doing some actual self-supported bike tours, but I'm unclear on what type of routes I can expect to tackle.
Obviously, I can do paved and gravel trails/roads, but will any type of single-track or dirt-path be unthinkable for great distances? I suspect anything with jumps is a bad idea, but that's probably true for any loaded bike. What other things should I look out for on these trails with a non-MTB?
As a follow-up, what can I do to improve my bike for these rougher paths? I have already installed Schwalbe Marathon Pro Tours (original continentals kept slipping in wet grass and getting flats at the sight of a thorn), which have some decent tread.
For context, I'm considering segments on the Ozark Trail in Missouri. If I can't reasonably expect to do this on my current bike, I'll be settling for the Katy Trail.