Yes, the coolant does cool the spindle, but you could use it lightly even when no coolant is running. I often run parts without coolant, but would not want to run it for hours at 7500 rpm. Also, if it is that cold there, it will probably not heat up anyway. The heat would probably dissipate very quickly in the cold.
You may want to check with your coolant provider and see what the freezing point is for your coolant at a given concentration. May not freeze at all.
Mike
Two Haas VF-2's, Haas HA5C, Haas HRT-9, Hardinge CHNC 1, Bother HS-300 Wire EDM, BobCAD V23, BobCAD V28