If a colder air mass blows over warmer ocean water, does evaporation of water happen quicker than earlier when the air was warmer?
All else being equal (wind speed, pressure, humidity, water temperature, sunlight, etc), warmer air corresponds to more/quicker evaporation, because there is more energy available to pay for the phase change from liquid to gas.
The phenomenon of seeing clouds of steam coming from comparatively warm liquids in cold air has to do with condensation. Water vapor is invisible. The smoky white clouds rising over warm water on a cold day are not water vapor but liquid water: countless tiny droplets of liquid water that has condensed after rising as vapor from the surface and then cooling and condensing upon exposure to the cooler air.
You don't see clouds rising from water on warm days because the warmer air can have more water vapor in it before condensation begins, that is, it has a higher dew point. The water is still there, but it's a vapor, so you can't see it.