On a 1999 A4 4 cylinder.
Can anyone tell me what the black connector next to the power steering reservoir leads to. On my A4, the wire goes under the front bumper and was cut off.

 

It looks like the outside ambient temp wire. Does your instrument cluster display the outside temp? if it does, then I'm wrong. It can be a fog light wire, a horn wire, a headlight washer, an AC pressure switch wire that goes to the front ac radiator, maybe an ac fan wire(but it looks thin to be a fan wire. Good luck...

 

I think that goes to a sensor on the AC condenser. Its just below the headlight on the opposite side. I don't think you can get to it without removing the bumper, but you might be able to reach it from below.

 

That's what I think too. An AC Pressure Switch or another device I mentioned. Thanks, I think It's what you said too .