You can bring small coolers (soft-sided types) only as carry-ons. They cannot be checked as luggage. They have to be able to fit underneath the xray machine.
I'm not a recent cruiser, but I asked DCL this question, and they said yes, if it's a carry on and is soft sided.
We bought the vey cool clearanced one at the Disney Store -- it's one of the best soft-sided collers I have ever seen. I'm kicking myself for not buying 2.
I can't imagine them restricting the use of soft coolers, esp. if you have small kids or a medical reason for needing a cooler. We need to carry drinks for my kids, and as a breastfeeding mom, I always carry around a big bottle of ice water. (TMI, sorry.)
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