When I live our rig for a longer period, like a month I train the fresh & grey as well as the water heater. I do leave 3-4 gallons of treated water in the black tanks. If it's freezing out then I leave the antifreeze in both the grey & black tanks.
Leaving your grey tanks open can be bad; as your dealing with sewer gasses. When I setup my dump hose I do try to create a bit of a U or dip in the line. I really hate having to monitor the grey tank with 5 people taking showers, washing and prepping meals. Some places I do leave it closed.