In Virginia, there are leash laws. On state and country property, all dogs must be on leashes unless specifically allowed off lead. On Federal land (national parks and such) they are designated off lead areas.
If the woods are privately owned, it would depend on the owner of the land.
However, citing laws is all swell and such, but, if your dog bites (or even threatens to bite) someone, in many jurisdictions it is up to the dog owner to prove that the dog is not a threat.. That is not an easy thing to prove.
"your dog bared its fangs at my child" is a pretty tough thing to disprove. Tie, unfortunately, often goes against the dog.
I always keep my dogs on a leash when out and about. Not because of my dogs but because of other people and other dogs. There are a lot of people who are either afraid of dogs or simply don't like dogs. I really don't want to make myself nor my dog vulnerable so some complaint where I am at a legal disadvantage.
Not fair, not right. But a reality.