We had our son's birthday party at a park in June.
We did hot dogs, and I boiled them before we left the house and kept them warm, but I didn't reheat them on a grill.
I'd personally not recommend doing the hamburgers unless you have your heart set on them. We were able to purchase 7 lbs of pulled pork from a local farmer's market that we warmed in the oven until the party (how I kept the hotdogs warm). It was way too much for the 40 people we had there, and I ate it for the next week. But, it was easy, required no prep, and allowed me to stay focused on the kids/party.
I'd always recommend having food already prepared so you can tend to all the other stuff that goes on unexpectedly - especially in an uncontained place like a park.