problems with enging cooling fan=still running

we have a 2008 toyota tacoma trd sport. All of a sudden we started hearing a high pitched sound when reving or idling. We think the engine cooling fan is stuck and keeps running. WE do not believe it should be running all the time, as it certainly is not hot this time of year. If the clutch mechanism is stuck, would it cause this sound. Is this normal for the fan to keep running. Is this a common problem and has anyone encountered this before, if so, what was the fix. The transmission seems fine. If anyone has had to replace this, what was the cost of a dealership doing it. We do have the extended care package for another 6 mos, but as it is the weekend, we do not know if this is covered. My truck is in great condition and is not abused. The odd horse towing now and then but it has the 6500lb towing package. Any advise or info would be welcome.