It's the batteries that don't do well in cold weather, and of course GPS units are battery-powered. Batteries discharge power when their negative and positive terminals are connected, something that causes a chemical reaction inside the battery, which in turn generates current. You'll recall from your basic chemistry class that chemical reactions slow in cold temperatures. So, as a battery cools, the reaction inside follows suit. Eventually, the reaction becomes so slow that the battery can't produce any current at all, and becomes, effectively, dead. Once warmed back up, the battery returns to life.
So the solution is simply to keep the battery warm. Carry the unit in a pocket, or keep a spare set of batteries in a pocket, and it will work fine. Of course, the wild card is whether you're in need of the unit on a constant basis—mounted to the dashboard of a snow machine, for instance. If so, then there are no good solutions—the only thing you can do is keep several sets of spare batteries on hand and warm, and swap them into the unit as needed. Maybe you could rig a heater unit that plugs into the snow machine's cigarette lighter (they have those things, don't they?).
That said, warm the batteries and your Garmin will work just fine way below zero. Or get a map.
Read more about the gear polar explorers need to survive from Outside Online's partner site, GORP.com, in "An Explorer Head to Toe".
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