I have an indoor swimming pool - can I have a large mirror, or will it be steamed all the time?
Are the walls wet? If not, then a mirror the same temperature as the wall it's mounted on will also not be wet, as the water is not condensing on the walls. 

If the walls are too cold and the water is condensing on the them, then it will condense on a mirror mounted on them, since that will also be too cold.

Constant fogging is primarily a problem (in my experience) where a poorly insulated mostly-glass structure is built over an originally outdoor pool. If your pool room is inside a house that's properly insulated, that's far less likely to be a problem.