Hi and

to disABILITIES!
I use a Pride Celebrity-X and one will fit in mine, but a lot may depend on both the cooler and the model of
ECV.
But if your cooler has a strap, as mine does, it can also be hung from the handlebars or on occasion I will put something on the floor under the seat. As long as I don't try to do turns at real high speed it will stay there.
(Also I have moved this to the disABILITIES Community Board as it really does not deal directly with Disney World.)