So many dog owners that contact me for help get so disappointed when I suggest they don't take their pups to dog parks. I don't even recommend taking adult dogs there either. When I talk about dog parks, or dog runs, I mean off-leash.
The reasons for my feelings on dog parks are simple. Dogs are pack animals, and when you have more than two dogs together, you have a dog pack. As I stated in my article on pack drive, we underestimate the pack drive of dogs. When these dogs are running together, they are establishing rank. Lots of time the dogs will work out their rank issues, but other times they will fight. If I'm the leader of my pack (my dog) I am not going to let my dog settle ranking issues with other dogs, whether they are part of my pack or not. For every person who tells me they never experienced a fight in a dog park, I bet there are five who have.
Puppies who experience a bite, pin or dominance from an adult dog can be affected for life! It can show dog aggression (fear based) forever.
I wouldn't let my pup socialize with any adults. The Pup should only experience positiveness. Bonding with you,trusting you as a true leader. The dog will grow with confidence.
You can do your dog a favor and keep it away from strange adults. Keep your adult on a leash when around strange dogs. Dog fights happen in a flash, and breaking up a fight between dogs unscathed isn't that easy. Prevention is the best medicine!
Socialize smartly. People, Places and things.
With all that said, if you have friends with dogs that all get along quite well then let them run together by all means. Just remember to clean your dog when done as dog parks can be filthy as well.