The AutoWiFi app I am using says it doesn't use up the battery because it isn't using GPS to get your location it's going off which cell tower you are connected to. I can attest that it doesn't drain the battery and it does work. During the day when I am out the WiFi is off and when I get home it's on. I would thing something like that could be used to turn the mute on and off.

I never even thought about auto muting. I don't mute it much. I think something that un-mutes after a time would be better anyway. Unless you go to the same places frequently where you want the phone muted.