Keeping washing machine lines warm in a cold garage
Instead of a space heater, try some pipe heating cable. This is a simple electric resistance heater that is designed to be wrapped around pipes in order to prevent freezing. The good ones have a thermostat built-in, so they'll only kick on if necessary.



You wrap the cable around your pipes, apply insulation over the wrapped pipes, and plug it in. This will be a little trickier around your washer supply hoses, but assuming these don't move a lot you can probably just use some duct tape every 6" or so.