I'm surprised that they are still using the Enfield though I can see the logic behind their choice. It is a very tough, reliable and reasonably accurate rifle. However, I think any of today's big-bore bolt action rifles would work well. In conditions such as those, I would really hesitate to recommend a semi-auto. I have seen so many jam when it gets really cold.“The roughly 4,700 Rangers-sprinkled in 178 communities across the North are the backbone of the military’s presence in the region. They conduct patrols across the vast tundra and are equipped with Lee-Enfields, bolt-action, magazine-fed rifles that were standard issue during the first half of the 20th century.”
The army has been running out of spare parts for the Enfields, making their issue unreliable as polar bear guns. It has been trying to purchase new rifles for several years, but has yet to come across replacements for these polar bear guns. The Enfields, though, do have one advantage that future polar bear guns will need to match.
“The fact they don’t freeze up or jam in the Arctic is part of [the Enfield's] charm, so the army made the decision last year to equip regular-force units conducting operations in the North with Lee-Enfields until replacement weapons arrive, possibly next year.”
When you have a gun out all day and then take it indoors at night, condensation forms on it. When you take it out the next day, that condensate freezes. Some oils will also become very viscous when cold and will prevent parts from moving like they should. If you have condensate/oil freeze in the firing pin channel, the pin will not fall or it may fall so slowly that it will not set off the cartridge. The action can freeze shut leaving you with a jammed single shot firearm.
Another option would be 12 gauge pump shotgun with 3" or 3 1/2" slugs, extended mag and an 18 inch rifled barrel with rifle sights. Brenneke sabot slugs are hardened and show impressive penetration. You can always rack a pump, even when the oil or condensate freezes. I've had to do it in -20 deg F weather.
A Keltec KSG would be almost perfect for that role, especially if equipped with a red dot sight and a good light. If a rifled barrel was available for it, it would be perfect. Having a rifled barrel will allow you shots up to 200 yards with slugs.