When your dealing with really cold conditions, it can seem like you are on Mars, and using space suits. As Canoedogs says, it can be a major project just to get dressed to go outside, what with massive boots, big parkas, hoods that form tunnels around your face, overpants, huge mittens. Buildings in really cold regions typically have an "arctic entry", which is sort of like an air lock. Once your outside, the darkness and ice fog can give things an otherworldly feeling.

Bush planes and helicopters don't like to fly when it gets below about -40 F (-40C), though they will in a life or death emergency. Materials behave differenty. Ordinary oil and hydraulic fluid tends to get thick, rubber and plastic gets brittle. Equipment meant for the arctic often use special steel alloys, since even regular steel gets somewhat more brittle.

As JBMat found out, in Alaska the coldest places tend to be the interior basins, such as the Yukon Basin or the Tanana Basin. They develop strong inversions, and there can be a big temperature difference between the bottom of the basin and the surrounding hills. There is a reason people in Fairbanks like to build their houses on the hills (hint: it is not just for the view). On the North Slope, the coldest I've experienced was about -60F (-51C) ambient, which was a near record low for Prudhoe Bay. That day there was just the very slightest hint of a breeze, and I absolutely could not look upwind, or my face would fall off!

Here in Anchorage, we have a strong marine influence, which tends to moderate temperatures. Typically the coldest we see in Anchorage is probably around minus 20F (-29C), and I think the record low for Anchorage is somewhere around -30F (-34C). The thing about Anchorage is how much the weather can vary depending on what part of town you are in. On the west side of town near the airport it might be -5F (-20C) and at the same time at roughly the same elevation on the east side of town (at the foot of the mountains) it can be fifteen degrees colder. When the Chinook Winds blow, it can be blowing 90 mph (145 km per hour) in the subdivisions up on the hillside, and be only slightly breezy on the west side of town.