How fun! Here is a thread with a couple of photos from a member who took their Yorkie hiking in the Shenandoah.
http://www.yorkietalk.com/forums/tra...henandoah.html
Cold weather would be easy to deal with. My bigger concern would be heat. September can still be very hot. A person in one of my dog groups on Facebook lost a German Shepherd to heat exhaustion while hiking.
Be cautious.