It does not need the ICE to run the A/C.  The A/C runs very well off the
battery, but occasionally, the ICE will kick in if the battery's charge
runs down.

I live in the Phoenix area, and the A/C is needed regardless of time of
day; it usually stays in the 90s all night.  I've had the car since
Thursday, and am getting mileage in the mid 40s.  I'm starting to learn
the gas-saving driving techniques, and have had some periods on the
highway with mileage in the high 50s to mid 60s.

Depends on which Prius you're talking about.

On the 2001-2003 Prius, the AC/defroster was belt driven off of the
gasoline engine.  So, AC use in summer is fairly similar to heater use
in winter ("waste" heat from the ICE to heat the cabin).  The fan will
continue to circulate the hot/cold air.  When the temperature of the
changes too much, the ICE will come back on to change the temperature
again.  (Just don't use MAX AC, and your system will cycle like this.  
MAX leaves the AC on all the time, so your engine runs all the time...)
Mileage won't be as good as if you didn't need to use the climate control,
but it's not outrageous, thanks to the cycling.

On the 2004 Prius, the AC/defroster is electric, run off of the hybrid
battery pack.  So, your engine doesn't need to run to power the AC.  
(Engine still needed for heat, however.)  If the battery charge gets
too low (about 2 bars on the gage), expect the ICE to come back on to
recharge the hybrid battery if you're stuck in a long traffic jam.

Go to this Web page to see the technical information on the 2004 Prius
air conditioning system.
http://www.denso.co.jp/motorshow/2003/en/presskit/product_electric/

GAN

No doubt about it, our 04 Prius gets less mileage during the heat of summer
than during the "cooler" southern months. The engine does not have to run
for the a/c to work, it is a completely electric system, like that used in
the back of recreational vehicles, so there is no mechanical linkage to the
engine. It does put more draw on the batteries, though. The engine has to
run more to supply more charge to the batteries.

Average fuel consumption:

Jan:  45.99 MPG
Feb:  Unable to determine
Mar:  46.91 MPG
Apr:  44.55 MPG
May:  43.62 MPG
Jun:  47.42 MPG
Jul:   46.79 MPG

Keep in mind that you'll get better gas mileage with consistant driving,
rather than stop and go driving in the city. As you can see, we seem to
average about 43 to 47 MPG regardless of the air temperature.

KK

I live in the Nevada desert, where it's over 100just about every day from
May through September. The A/C doesn't change my mileage enough that I have
noticed it. And, no, the new Prius doesn't require the gas engine to be
running. It's a very efficient electric unit...