How to keep things like ice cream bars and cones cold without freezer?

You can't unless you have dry ice. They wouldn't be edible without being kept frozen. Possibly, if there's electricity, you can get a small freezer.

Try filling a large cooler with ice packs or bagged ice in order to keep the ice cream cold. Most grocery stores and local convenience stores sell bagged ice, unless you want to make it using your freezer at home. You could fill empty gallon ice cream buckets with water and freeze them as large ice cubes. We do this quite often when going to a picnic or having a party at the house where we need to drink drinks or food cold for extended periods of time.

You can use dry ice as a refrigerant but you need to keep the trailer ventilated to prevent a potentially dangerous buildup of carbon dioxide gas in the trailer.

I have taken ice to to functions where there was no freezer. Put on block ice and it will stay frozen all day.