In the course of my daily commute I normally ride my DT Mini for about a half mile of the towpath of the Delaware and Raritan Canal (in New Jersey), which is not paved. No problems there, but the pedalling can be pretty hard work when the trail is muddy (this is true on all bikes, but both narrow tires and small wheels seem to exaggerate this effect a bit). Last week I rode the same bike on about a mile of the bridle path in Southhaven County Park (on Long Island); there I bogged down in the sand a couple of times, which was a nuisance; but no real problem. I had to go over a bunch of roots, which was okay (I took 'em slow), and some loose pebbles (they shot out from under the tires when I hit them) ... but again, no problem with due caution. I did not encounter any steep hills, and I don't want to; I am a wimp about that sort of thing.

So yes, I think a folding bike can handle trails pretty well, assuming the surface is hard enough and you adjust your riding style to suit conditions. In other words, slow down, hold tight, and keep on pedalling, and you'll be fine.