Four months old? Isn't that within the critical age range where pups are especially vulnerable to negative experiences & can have longterm consequences?
My prior dog always ended up on top of the picnic table when I took him to the dog run. He clearly didn't like the run so I stopped going. But, what triggered his fear aggression was a horrible experience where an off-leash dog attacked my dog out of the blue while I was walking him on leash in an on-leash park. Recently happened to a neighbor who adopted a puppy mill rescue - she was teaching the dog how to walk on leash when an unleashed dog ran over & attacked the poor thing. Now the dog doesn't want to go outside at all.
With my current pup, an english shepherd, I waited until she was about five months & had many pup socialization classes under her belt before taking her to the run. I go on a semi-regular basis but do not feel 100%. While playing, she will sometimes dart under a bench to get away or take a 5 sec break & then rejoin the group.
Not sure if it is fear or just a diff play style - given her very primal cow/sheep herding lineage, theoretically, other dogs "shouldn't" frighten her. And, being a herding breed, she prefers chasing to wrestling or boxing, which the many retriever-type dogs at the run prefer. At times, it looks like my dog would prefer to referee the play than actually participate. She also loves to make her rounds & say hi to all the owners.
My other concern is that, at 7 months, she is a nice size gal, weighing around 50 pounds. The weight differential between her & the tiny dogs worries me - she is a sweetie & has a size appropriate play style but an accidental bump could easily hurt a small dog which, of course, would be devastating. At the same time, my pup is high energy & needs exercise so I am conflicted as to whether to take her to the run or not. I recently splurged on a dogpacer treadmill to supplement her exercise and hoping that between the treadmill & agility classes & long walks/hikes & mental training, I can meet her needs.