Wow......
Lots of people here don't really understand aircon, don't get me wrong lots of people have a good idea but there is a lot of miss information in this thread.
MEP kept trying to make a very valid point, just because the ac light is on doesn't mean the compressor is active.
So on starting as pointed out the compressor clutch is disengaged until the canbus system is happy the engine is running, sometimes you'll hear the compressor click in a second or so after starting. So it should never stall a car especially a 1.3mjd
Once running the system will cycle, so the compressor will get the pressure up in the system and once there it can take a while for the high and low pressure sides of the system to equalise, during this time you will still get nice cool air but the compressor will be switched off, you'll notice this more on cars low in gas as the air will get cold and warm with the cycles.
Wide open throttle the ecu will cut the ac (usually anything above 80% throttle) this prevents the aircon sapping power when you need it.
Efficiency issues, a fully gasses system is most efficient as it won't take the compressor long to get up to pressure and it takes the longest time for equalisation, remember during this period the compressor is off. A system low on gas my need the compressor running constantly which will have a major effect on fuel economy.
The difference in hot and cold weather. It's a long explanation so bare with me...
In hot weather the compressor pushes the expanded gas, adding energy, into the condenser to be cooled down to remove heat energy, before passing to the expansion valve, when the gas expands loosing more energy and thus loses heat getting very cold and passing through the evaporator where it takes the energy out of the surrounding air, making the air cold and the gas warm again. The gas then goes through the receiver/dryer to remove any contaminants or moisture in the gas and then back round to the compressor to begin the cycle again.
On a hot day the gas is already carrying a lot of energy, the compressor has to work hard to compress the already expanded gas, the condenser then has to work harder to remove more heat, when expanded in to the evaporator the gas is faced with hotter air and so more energy to exchange, meaning the gas is heated more and expands more, before passing to the dryer and back to the compressor
On a cold day. The compressor compresses the gas and it still gets hot, however the condenser is much colder and cools the gas much easier, it then expands greater when passing into the evaporator (much greater pressure differential) and so the gas more easily exchanges heat with the air in the cabin. The gas doesn't take so much heat out of the air because the air is already colder and so the gas does not expand as much on its way out of the evaporator. The denser gas passes round to the compressor which finds it much easier to compress the denser gas.
The upshot of this is that on a cold day the aircon draws a lot less power from the engine than in the height of summer, even I the compressor is running for the same period of time. No different to an alternator charging an empty battery will use more engine power than an alternator attached to a fully charged battery.
Cooling already cold air is easier than cooling hot air.
So in the winter running your aircon will use very very little extra fuel. But the cold evaporator will cause any moisture in the air to condense on its surface which drips into the drain and out through the bulk head on to the road. This takes the moister out of the air that would other wise be steaming up the windows. Hence why aircon clears the windscreen much faster then non aircon. On the flip side on a hot day the aircon will be more demanding an use more fuel.
Someone mentioned air con servicing. And replacing the dryer, just to make a point the 'dryer' has nothing to do with drying the air, it's just following replacement of these parts the system was working better and a nice cold efficient system freezes the bugs and stops the damp musty smells by efficiently removing the water by condensing it on the evaporator (confusing I know) A poorly working system cycles cold condensing the water then warm giving the bacteria a nice wet warm safe haven. A clean pollen filter is good but doesn't need changing every year, (every 3 is fine) check the drain is clear and not blocked and being well gassed is sufficient,
The best test of any air con system is on a hot day (+20degreesC) to check ambient temperature, then measure temp at the vents, anything over a 15degreeC drop is perfect. No need to do anything else.
Properly cycling the system summer and winter will prevent the bacteria and smells saving wasting money on air con cleaning chemicals. In winter the system is designed not cool below about 5degreesC to prevent the moisture freezing. Another reason it won't use so much extra fuel, compared to summer)
This leads me on to the automatic climate control,
These systems when set to auto, are supposed to wait for warm coolant to be available before blasting the fans. The aircon light being on simply means the acc is managing the switching of the compressor, it will turn it on and off as needed but will operate all the time to aid with demisting in cold weather and cooling in hot weather, but this is obviously managed with regard to the temperature you set on the dash so will be more efficient then simply running the aircon all the time in manual mode as once the desired temp is reached it will cycle off the aircon and slow the cabin fans. If you are warming the car against cold external air, the aircon isn't hardly much energy anyway.
The fiat ACC system is however crap and is very slow to respond to changes in temperature. Which is why people get frustrated with it. So you set it to 20, the car heats the air to 20 but takes 3-4 mins to realise this and when it does the temp is 22 and so it then starts cooling down to 18 then back up to 21 then down to 19 blasting the fan speed up and down and generally being annoying, before eventually settling at the desired temp by which point you've already gotten fed up and switched it off auto to control the fan speed yourself.
I probably could ramble on some more but I will leave it there, basically aircon systems are simple in the way the work, but complex in the science, they are self managing in regards to energy use, which is dictated by ambient temperature, at either end of the system, they don't run dumb and just consume power all the time.