For most commercial jetliners (the kind I would expect over the arctic) the air conditioning power uses engine bleed air. Very hot, high pressure air from the core of the jet engines (or the aux power unit) is bled off and used to drive the air compressors that provide cabin pressurization at high altitudes and air conditioning (cooling) at lower altitudes. Bleed air is also available to heat the incoming air and can also be used to heat the leading edge of the wing to prevent ice build up.

Most of the time cooling is a bigger concern than heating since there are lots of electronics and passengers aboard the plane that produce a lot of heat.

-Eric