This reminds me of an anecdote from a local (European) telco:
A customer called the customer support line because their monthly invoice was way higher than in the previous months. They had 3G data access modems/SIMs and a fairly standard contract. The CSR searched their record and found that they had a lot of roaming data fees (really expensive if you don't have a special contract). The customer then replied "I see. Well, we use these data SIMs in special collars to monitor some bears... One of them went abroad."
The collar sends its location every 3 hours = 7 times per day = 2555 times over a year, for a couple of seconds each time. If on average each wake up lasts 5 seconds, that's only 3.5 hours over the year, so definitely within the range of commercial batteries.
Even with A-GPS, a GPS fix takes longer to obtain, and data transfer with GPRS takes ages... add the space constraint of a collar, and it becomes really complex.
OK, so assume the GPS receiver takes 60 milliwatts [1] for 60 seconds, four times a day. You'd be using 0.66 milliwatt-hours per day. (Other receivers claim to use as little as 8 milliwatts [2])
A D cell alkaline battery, depending on the manufacturer, can have 20,000 milliwatt-hours or more [3].
Two of those and you could have 4 years of battery life. Assuming your batteries retain their advertised capacity when dragged around in snow and ice by a wolf for a few years!
Temperature certainly has an effect on batteries¹. But also that the periods of high current demand were spaced so far apart -- the batteries had time to recover. Much like how the battery in your car is a "starting" battery -- high current is needed only occasionally to start the engine, with the alternator making up the demand the rest of the time.
¹ Dad used to work for Union Carbide, which owned the "Eveready" brand at the time. One of the projects he worked on was a battery for the Union Pacific Railroad. It was designed to be buried in the ground in remote locations to run signal systems. Burying it gave it a more constant temperature. If the researchers placed the battery on the inside of the collar next to the wolf's fur, that could really extend it's life.
Ah, spotted an error there. If you were using 0.66 milliwatt-hours per day and had two 20,000 milliwatt-hour batteries, it would of course last for 60,606 days. Which is 160 years not 4 years.
Of course, you'd also need to power the radio module to send the SMS, and presumably wolves spend time in remote regions with poor cell phone coverage Products like the Quectel M10 can use as much as 2 watts while transmitting [1] (or as little as a fifth of that). To make 40,000 milliwatt-hours of batteries last for 5 years would only give you a budget of 21 milliwatt-hours (75 joules) per day. That would let your run a 2 watt transmitter for about 37 seconds a day - so to make 8 transmissions a day you'd have to power on, join the network, transmit, and power down again in less than 5 seconds.
On the other hand, according to [2] it takes between 1.5 and 5.5 joules to send an SMS, allowing us to send several in a budget of 75 joules per day. They don't make much mention of signal strength or the energy cost of connecting to the network, unfortunately.
So I guess it all comes down to how long you have to have your radio module turned on in order to get a message off.
There are also tracking collars with solar cells [3].
With a cold start - yes. But most GPS chips have memory backup for short-term almanac data (valid for up to 4 hours, works if the GPS doesn't move long distances in that time period) and internal clocks, so it can perform a warm start. This takes only a few micro Amps standby current, so it's not hard on the battery.
I doubt this is the case, but you could have sort of charger to keep the battery topped up that was based on the automatic winding mechanisms of some watches.
It's a different species, cougars, but this is an interesting story of one that was killed by a car in Connecticut, and which was identified as having come from South Dakota, 1,800 miles away.
I tracked down the manufacturer in another comment. Their devices can communicate with UHF/VHF radios, GSM and a couple of different satellite systems, Globalstar and Iridium.
A customer called the customer support line because their monthly invoice was way higher than in the previous months. They had 3G data access modems/SIMs and a fairly standard contract. The CSR searched their record and found that they had a lot of roaming data fees (really expensive if you don't have a special contract). The customer then replied "I see. Well, we use these data SIMs in special collars to monitor some bears... One of them went abroad."