Jirams makes a valid point. And, as they say in Yorkshire, 'you don't get owt for nowt.'
It's a question of how much extra fuel is used. For my Jazz I don't know... The motoring industry traditionally claimed aircon uses 5-10% extra depending on make of car and motoring conditions. However modern aircon systems, and particularly electric ones (as my GE Jazz has, if not GD, too), are reputed to be more fuel-efficient if I recall correctly. But by how much??
Jazz does not have a particularly powerful aircon system though, as with everything (IMO) with this great all round, versatile car... it is adequate. When the fan kicks 'on', my tacho needle barely momentarily dips... markedly less than other cars I've run. So (hopefully) those are signs it may use less fuel than p'raps some other cars do.
After 20,600 miles my GE1.2 Jazz displays 54.3mpg 'average' over those miles, air con always 'on,' mixed motoring, a good part of it fully loaded and 75ish mph when on the motorway. It's the only car in our household, so it does all sorts.
Months ago, out of curiosity, I switched my aircon 'off' in the middle of pulling up a steep hill - intentionally letting the Jazz labour a little which I wouldn't normally do - and if there was any increase in pulling power, I'm blowed if I could tell. I tried it again on another hill, still couldn't tell.
So you might deduce that mpg with aircon is an interesting question for me, too. If anyone has a measure as to how much extra fuel Jazz aircon uses, I'd certainly be interested to know. I should do a comparison measure over some miles but I suspect there are too many motoring variables.
For sure, a/c systems are expensive to fix and a broken one can considerably effect resale value.
In New Zealand where I spend a deal of time, a number of people I associate with don't think twice about leaving aircon permanently 'on' throughout winter. In fact I don't think I know anyone - private car owners, too - who switches it off. It may not be a representative sample but these particular NZers (at least) likely don't see aircon components' service life as an issue. Their fuel prices, too, are virtually same as UK when wages are taken into account. By and large, many NZ winter days are not warm enough as to require it 'on' either. But aircon does keep the interior of a car dry and windows demisted.
Nevertheless, you don't get owt for nowt as jirams has suggested. P'raps, all things considered, best policy for components' life and minimal fuel consumption is to be sure to run aircon at least 10 minutes a week throughout winter. P'raps, too, I should try to get a measure on aircon fuel consumption.