On your Range Rover the air con is always on unless you physically turn it off with the air con off button. It's the fastest way of clearing steamed up/fogged up windows. Air conditioning does what it says, it conditions the air. It dehumidifies it, and by virtue of the fact it fridges it as well it kills a lot of bacteria, though these will grow on your evaporator. It works with the heaters on any temp and will help to keep the inside of your car dry. As for the economy side of things, on a car as thirsty as a 4.6 p38 it makes pretty much naff all difference, especially as it's a modern day system that cycles the compressor on and off. There always used to be a thing for removing the belt on cars to save fuel, but seeing as with the compresor off it's just an idler pulley that makes sod all difference as well.
A lot of big engined cars like V12 jags, Rolls Ryce and Bentley etc also rely on the air conditioning for fuel cooling. Disconnect the air con, no fuel cooling leads to a massive increase in evaporative losses and actually costs you more than if you where using the system./
Having worked in the prestige vehicle sector all my working life it does grind a little when people buy a big luxury car with a big engine and then gripe about the amount of fuel it uses. Changing your driving style and keeping things maintained is far the biggest fuel saver.