This light is directly connected to the float sensor found right under the cap on the overflow tank in the front of the engine bay. If the float drops down below 'full' level, the light comes on.
Check your fluid, if its only slightly low (ie. theres still enough left in the tank for the sensor to be floating some), top it off with water or 50/50 coolant. Check to ensure that the coolant is that nice limey radioactive green color and is not brown or muddy with oil. If you see oil in your coolant- that means the missing coolant is escaping through gaskets shared with oil passages (head gaskets).
Check your thermostat housing (at the end of the upper radiator hose, with the 2 long studs protruding). If its got coolant on it you should replace your thermostat and thermostat gasket. Also verify that the black plastic intake is not cracked around this spot. There are problems with every mustang with this intake cracking there.
Try checking your fluid level. Perhaps even flushing it out and adding a whole new mix in there 60% antifreeze, 40% distilled water or 50%/50% (i prefer 60/40 in the winter, it protects against lower temps than 50/50). At 60k miles i think its a good idea to do a radiator flush.
Its also a possibility that your radiator cap/float sensor went bad and just needs a simple replacement.
Most likely when that lights comes on though, its because your coolant is low. And like Triggz said above you might have a leak somewhere..although if your headgaskets are leaking into cylinders you would be getting a white smoke out the back of the tailpipes.