How common are diversions to high-latitude airports for intercontinental flights?
Very very uncommon. Goose Bay, Canada, is a diversion airport for US-Europe flights. If you search Aviation Herald for "goose", you will find about 2 to 3 flights divert there each year.


3 flights diverted in 2017:


Delta A330 Oct 20, engine problem 
SAS A340 April 16, low cabin pressure 
Air France A380 Sep 30, engine structural failure


2 flights diverted in 2016:


Virgin B787 Nov 22, engine oil leak  United B767 Sep 15, generator/APU failure


3 flights diverted in 2015:


American B757 Sep 30, electrical problem 
Delta B767 July 31, generator failure 
United B767 June 12, flight controls


2 flights diverted in 2014:


Delta B767 Aug 9, engine problem 
Delta B767 May 1, engine shut down

In all these incidents except for 2, the report in Aviation Herald states a replacement aircraft was required. Sometimes the delay was 6 hours, sometimes the next day. In the 2 other incidents, it's unclear if a replacement aircraft was required or not, but in both cases maintenance was required, so at least a delay occurred.

This compares with a bird strike, or fumes/smoke in the cabin, almost daily somewhere. It's much rare than even lightning strikes, of which 25 were reported in 2017.