So an outdoor bathroom needs to have all materials that hold up outdoors I assume you live where the wether is good year round so just think water proof fof floor , no vanity just a pedestal sink maybe a wall cabinet in steel painted probably vinyl flooring . As for the AC how hot does it get where you are ? Maybe just one of those portable AC units .

No I'd do tile flooring and AC depends where you live.

I am thinking a bathroom that is used when outside enjoying the pool or outdoor activities.

Clerestory windows, some low venting and a ceiling fan should keep it cool enough considering you are sitting outside in the heat.

Flooring needs to be water resistant and slip resistant as people are likely to run in wet from the pool. You may want to consider using the same material as you are using around the pool.