Typically only when cutting metal. And harder metal especially. Wood and the like will often have an spray of air directed at the cutting bit but thats simply to help clear away chips and clean the cutting surface. Helps keep a nice finish and good visibility.
Actually, it's a little different. Using coolant is the norm even when doing mild steels. You can remove material quicker, your part remains cooler, and your tools remain cleaner.
There's even cuttings bits that have integral cooling (holes in the cutting surface).
Right--I support a fair number of machine shops and they're all moving to CNC (although they're using a lot manual machines still). 5 axis is nice and there's a surprising amount of manual tooling changes.
We had a problem where one of the integral cooling loops had a tube come off and it sprayed the better part of a 50 gallon drum of coolant all over the shop before someone got over and hit the e-stop.
Pretty sure even the mildest steel is still a hard metal. Soft metal would be something like copper or aluminum IIRC. (Or lead or gold, moreso, but you probably wouldn't want to be machining those for obvious reasons.)