I have a large amount of vinca minor, which I think would be a good choice for you. It's low-growing, reaching about an inch at maturity. It's also vine-like, with long trailing stems that cover the roots of even your biggest trees. It has very shallow roots, so even if it gets near your path, all you have to do is pinch it back or pluck it out. The dark oval-shaped leaves are pretty all year round. Lovely, low-lying purple/blue flowers bloom profusely in the spring and fall, and sporadically through the summer.
Vinca is hardy in zones 4-8 (I'm in 6), tolerant of most types of soil, especially the type of moist ground that's common under trees, and is very easy to grow. Even though it's mostly a shade plant, it thrives in some sun, and I use it as a border behind some sunny annuals like marigolds and salvia.
It also transplants very easily. This year I pulled some out, stuck the roots in potting soil and it became a really pretty trailing element in my shade-growing window boxes, where it's held its color all winter.
Some people call it invasive, but for me, that's a good thing. As you can see from my picture, it quickly fills in any space. It will also wrap around sedum, hostas, and any other shade plants in the area.
Click on picture for bigger view.