All of my mills have built in coolant pumps. I use Castrol Hysol XF as a coolant and I keep the mix correct with a refractometer. How I use coolant depends on the mill.
CNC: I always use flood coolant (except for cast iron, brass and plastics) primarily to wash the swarf away rather than cooling the mainly carbide cutters.
Horizontal: As for CNC, except mostly for cooling as I only use carbon steel and HSS tooling.
Vertical: I almost never use coolant since there is no drip tray and the stuff gets flung everywhere. I wouldn't worry if a HSS cutter was running with the swarf coming off yellowish. For carbide tooling anything goes, the swarf is normally at least blue in colour and when running hard the cutter has a hint of red in subdued light.
A summary is that for carbide tooling I almost never use coolant (except for the CNC mill) and for HSS tooling I almost always use coolant (except where the material doesn't need it or on the vertical mill).
Complicated isn't it!
Andrew