Can police locate a person by tracking their mobile phone? ?

It depends. If you have location-sharing on, then YES.
If your phone is in emergency mode, then yes.
If you have the location-sharing turned off, they have to go through certain procedures to track you, but it can be done.
Generally the phone has to be exchanging signal between itself and one or more cell phone towers. Usually a cell phone will lock in on one tower for as long as it can.

ANY signal can be tracked by triangulation if the right equipment is in place and the signal is transmitted long enough.
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EDIT to correct wrong information by other posters;
They don’t need helicopters or SigInt (signal Intelligence) vans. They can rapidly receive and enforce court orders for the cell phone companies to list which towers are receiving signal from your cell phone and what the distance is from the point of origin to the point of reception. The only time that mobile transception devices would be needed is if you are in an area with very little signal reception, though in most cases those “holes” are isolated enough that if your signal’s distance is known, you can be found quite rapidly.
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The location feature on the cell phone should be active in any 911 call. The fact that climbers on Mt Hood have not been located in time is probably largely because of the remoteness of their location, but it is probably affected by the duration of their batteries and the variance in the strength of their signal with the temperature-varied strength of the output from their batteries. Also, if the police don’t know the climbers have a cell phone on them. If it is turned off or incapacitated by moisture (Snow is moisture, and the heat generated by the phone will melt that snow enough to get water inside the phone), it can’t be much help except as a paperweight. Another issue there is that hypothermia and other cold-related issues affect the mental faculties much the same way as alcohol or other intoxicants, so it would be interesting to see how their resultant actions might have affected the duration and consistency of their signal transmission. Another point is that no rescue method is perfect.

The tracking devices are great, and they are probably specifically designed for the extreme environmental conditions encountered on a mountain during a winter storm.
That has nothing to do with whether or not triangulation of cell phones works, but it does prove that triangulation of some type of signal is better than none.
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Locating by triangulation is good enough that a sniper could hit a terrorist trying to detonate a bomb without even seeing that terrorist. GPS has nothing to do with it, although if it is turned on, there is an entirely different process of finding you by your pre-authorized location sharing, which does not require judicial or military intervention.