Weed killer will only kill the small plants and grasses, as mentioned by others. If you don't have heavy equipment, a small push mower with blade set as high as possible can do a nice job of making a trail. Then, deer traffic will keep it open.
Incorrect. We use Roundup (Accord actually, same chemical though) all the time in forestry to site prep conversion sites (hardwood to pine) to control the resprouting of hardwoods. It's highly effective if applied correctly. Also, it has minimal effects on wildlife, otherwise it would not be approved for this use, especially if you're using stump application. Haven't seen many deer gnawing on tree stumps.
I've used it on our own land to control resprouting on trails after we've trimmed them back with saws. Some species like alder, aspen, red maple, etc resprout vigorously after you've trimmed them, so you'll have twice the job the following year if you don't control the sprouts. Stump application with roundup works great to control the sprouts.