Short answer: yes, they can hold it and keep it cold at Bell Services.
But I'm going to be the voice of dissent here. I would never trust leaving my medication that needs temperature control. Maybe it's my bad luck, but if 99% of people have never had a problem -- I'd be the 1% whose item is misplaced or doesn't get refrigerated. I've had to get emergency refills of medications while on vacation and it isn't fun; it's a hassle, time-consuming and expensive. You say it will be in a cooler -- is that a lunchbag-style cooler or something else that you could bring to the park with you? I would prefer to bring it with me, refilling ziploc bags of ice if necessary. I suppose that may depend on the type of medication and the required temperature, dosing schedule, etc. But I would just prefer to keep it under my own control and not trust something as important as medication to someone else.
Enjoy your vacation!