Each district has its own restrictions. Most of them are the same, with a few minor exceptions. You’ve got a couple of options.
1) go to
VCDD What's Happening and look up each district’s restriction.
2) ask your realtor what district your prospective home is in and look up the restrictions (dont rely on realtor’s word as to what is allowed).
3) utilize an invisible fence, which is allowed in all districts, as they are below ground.
I will note that most areas do not allow fences, as villagetinker has mentioned. Depending on the size of your dogs, they could be considered prey by the wildlife here, and should not be left outside alone. In some cases, they should not be in your yard without a leash. That’s because you’ll be able to pull them away from wildlife that tries to grab them.