I moved this thread; no big deal, but it's a better fit here.
Those trails are what's known as the Burdocks. They are 'hobo trails,' not authorized or officially maintained by anyone, but used and maintained enough to be usable. This is the biggest network of them in town, but they are all over if you know where to look. This time of year is hard; the weeds are at their tallest, starting to fall, and the burrs are, as you noticed, out in force. They rely on folks like yourself getting out there and getting it done. Looking for help here is worthwhile. The crew at Revolution Cycles has some folks who put in some time there; it might worth it to stop in and talk to them if you want to organize something.
We can't loan out power tools for this kind of work. In general, power tools are maybe not a great idea on this kind of trail. Landowners who are willing to look the other way about bikers and hikers often aren't as mellow about strangers using chainsaws. Axes, handsaws, weed whips, hedge trimmers, and scythes are slower, but they are cheap, quiet, and have no exhaust.
There is a movement beginning to try to bring these trails above board. Perhaps this thread can get a few people together who are willing to make that happen. It will take some work, and maybe not be as immediately satisfying as clearing the trail, but in the long run will be a great service to our community.