I hike with a guy who trains and certifies SAR dogs. I find it spookily amazing when one of his dogs is with us. These are the most well behaved, totally confident, un-rattle-able dogs I've ever seen. They literally ignore you and other dogs unless told to do otherwise.
However, since 1993 (when my backyard became a nature preserve), I've been attacked three times by big loose dogs, bitten once. There is such a cross section of dog owners that use preserves for their dogs, that I simply don't trust any of them, and my dog trainer friend agrees. His dog was attacked by a pit bull terrier, in my park! He now carries a pistol in case it happens again.
I go armed as well, when doing trail work. Our animal control officer recommended I do, since that's what he does.