This is my bathroom (due to be renovated soon but it will keep the power outlets. It's the original bathroom from 1965!). We also run an electric heater in it as well, but it is always removed just before we shower. Old habits i guess.
I have bad experience of electric heaters in the bathroom. Years back I had a boyfriend whose young sister (she was 8) was electrocuted and died when she got out of the bath. My boyfriend had plugged an electric heater in for her as she was complaining it was so cold. I'm not sure exactly what happened but I know my that boyfriend never forgave himself. He committed suicide some years later. Its a tragic story.