No particular reason I want to know this, just curious. Can't find anything online (not even estimates). Anyone have any idea?

Nope.

https://en.wikipedia.org/wiki/Arctic_Circle

IF wikipedia is correct, about 4 million people.

Huh, that's odd. I don't remember Wikipedia saying anything.
Interesting.

300 000 of them live in Murmansk, the biggest city north of the arctic circle:

https://en.wikipedia.org/wiki/Murmansk Although apperantly Murmansk population is rapidly declining

"Very few people live north of the Arctic Circle due to the cold conditions. The four largest communities above the Arctic Circle are situated in Russia and Norway; Murmansk (population 307,257), Norilsk (175,365), Tromsø (71,590) and Vorkuta (70,548)."

https://en.m.wikipedia.org/wiki/Portal:Arctic/Statistics