To counter the effect that the cold has on electronics and more specifically batteries is simple in theory, you need to keep the battery warm. In reality this can be quite hard.
How Batteries Work
When a circuit between the two terminals of a battery is completed, the battery produces electricity through a series of electromagnetic reactions between the different components of the battery. The reaction in one part of the battery creates electrons, and the reaction in another part absorbs them. The result of these reactions is electricity. The battery will continue to produce electricity until components of the battery run out of the substance necessary for the reactions to occur. These reactions work in one direction.
Rechargeable batteries work in the same fashion but when plugged into an outside power source the flow is revered and electrons are added back to the source (recharging them)
When you take batteries out in the extreme cold like you get in Alaska this reaction is slowed down to the point that the reaction stops. This stops the flow of electrons and therefore the electricity stops powering the device.
This can be a minor inconvenience in cases of cameras, on up to a serious issue if its your GPS and you have no other navigational tools or skills.
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What Needs To Be Done
To counter this effect on the reaction is simple in theory you need to keep the battery warm. In reality this can be quite hard. If the device is not needed often, you can keep it deep in your layers close to your body heat and that usually does the trick.
If it’s a device you need to use often this may or may not work. You can always keep them in your layers or in a special pouch when they are not in use but when you take them out they wont last long.
What You Can Do
Depending on the device you have a few options,
Use devices that take conventional batteries (AA, AAA) and stick to none rechargeable. In our experience non rechargeable batteries seem to last longer in the cold. Carry replacements in your layers. In order to split the difference between burning through a lot of batteries and racking up the cost, We always have rechargeable batteries in our devices that take conventional batteries and carry non rechargeable spares if the device goes dead before we are done.
If the devices use battery packs like a phone or go pro for example, you can carry a lot of replacement batteries kept warm in your layers and swap them out as needed.
If the devices have non remove-able batteries you can plug them into a large battery pack re-charger to try and keep them charged up and keep the battery in your layers why the device is in use.
This last tip we do for all our devices regardless of what kind of battery it takes because it can help prolong the life of any battery and that is attach a heat source.
This is done with chemical hand warmers. We use either a rubber band or in the case of our phones an elastic tether that we can slip the hand warmer in behind and hold it next to the batteries. They hand warmers do require oxygen to work so if you bury them deep in your layers or gear they may not work for long so keep that in mind.