Contains spoilers:
Just why? So many odd plot choices. Why is the perp like he is? Why go to the cold place apart form the odd plot point about the frozen body? The perp seems to get there on a ferry with a bound hostage in the back and clear windows. Luther seems to take the next short ferry which is shortly after the last one and had to get in the boot. They wander about in a shirt and jacket off into the snow. The ice is somehow only 2 inches thick and had 100s of bodies - why don't they decompose in the summer?
A helicopter comes from London and later takes Luther back to a London hospital, why not somewhere closer? And somehow has enough fuel for a journey like that. It was also carrying divers that knew where Luther was under the water, and didn't have cold weather gear.
I am usually able to suspend reality, but this was just odd.
It would have been an good film if they had just wound it in. A lot.