OK. The only thing electical with the AC system is the compressor wiring, which is under the hood and dash (fuse panel, harness, etc.) and would not come from your vent, and the blower motor itself. Since the blower motor is working even when you turn the AC off BUT the 'smoke' stops and you don't smell it, it is probably OK too. You said that when you turn off the AC, it eventually stops. This is probably due to the air inside the vent system warming up above the 38 to 40 deg F required to condense moisture from the air. It would still feel cold, but not cold enough to cause the mist. Also, notice if it goes up or down as it comes out of the vents (fan on low). Fog will go down, smoke or steam will rise.
I would bet if you turn it to the recirculated air setting, the fog would eventually go away also, because you would be recirculating the dehumidified cabin air instead of bringing the outside air/humidity through the system. This would prove the AC system is working properly.
My Jeep and VW do this all the time. Again, you can smell smoke (or antifreeze if the heater core is leaking), but you cannot smell water vapor, fog, etc.