Iron golems can't float and/or swim and just sink to the bottom of any water source. They will do this very commonly if a lake/river/body of water is within or near a village. They walk into the water and sink. Screenshot is provided below. They do not take damage but also do not move and cannot get out.

My recommendation is they will avoid water unless their pathing requires it, and are able to swim out of the water. (Maybe they could even rust if put in water for too long?)