For most people, refrigerating fresh fruit cobbler is a good idea. “Fresh” generally means just that – the food is not processed or cooked for shelf life purposes. In terms of safety, fruit cobblers are relatively safe to consume because the processing was done prior to being served. When properly packaged and stored in a cooler, open desserts can remain fresh for up to 24 hours without requiring additional cold storage, but most people prefer the flavor if it’s brought back to room temperature before eating. It also makes packing a picnic much more convenient if you don’t have access to a household refrigerator or freezer on site!
The one major exception is custard-based dessert recipes like crème.