Thinking on this some more....
You may want to look into the root cause of this failure. The AC pump uses the AC fluid as a lubricant AFAIK - so no fluid & the pump siezes - so if your AC has leaked then this could well be the cause of the failure. If that is the case you'll need to find the leak before you replace the pump and fix that as well. Could be anywhere in the pipework or, worst case, the evaporators. This unit is buried in the heater box & to get to it you have to practically remove the entire dashboard. A £1300 job at a main dealer. (I am assuming here that the design is basically the same as my 96 A4 which has a very slow leak in the evaporators - I need to get the AC recharged about once every 18 months.) As one tech explained it to me - they build the floorpan, stick the heater box on it & then build the rest of the car around it!
If you are going to attempt to replace the AC pump yourself then come what may you should take the car to an AC place (or get a mobile guy to come to you) & get them to drain the AC system first. Then ask them to test it for leaks. They should be able to tell you how much fluid they were able to retrieve from it which will give a good indicator as to whether a leaking AC system is the root cause of your problem even before they test it. They test it by pumping it full of some kind of gas and then look for leaks with some kind of wierd gas detector.
You'd then need to get a mobile AC guy to come out & recharge the system for you before you start the engine again. I wouldn't drive the thing even a short distance with a new pump & no fluid.
In considering all the relevant costs bear in mind the warranty you will get on the repair if you have the work done by a dealer.
Bottom line, if your AC won't blow cold air then get your system tested for leaks or recharged before your pump siezes....!
HTH
I.