Daas,
The reason it is not a simple kal v’chomer is that there are two dinim. The chiyuv to cover hair is a separate din with a different limud than the chiyuv to cover other parts of the body (although the reason governing other parts of the body applies to hair as well).
A woman has to cover her hair in public even if that public consists entirely of other women, and even if she lives in a society where it is the norm to walk around with uncovered hair.
My knowledge of how frum women conduct themselves at pools comes entirely from reports from my wife.