Normally, there are Finnish buses from Karasjok to Rovaniemi in winter.
www.eskelisen-lapinlinjat.com/fi/index.php
Then a Norwegian bus from Kirkenes to Karasjok.
You can, but it's not very practical.
A Finnish bus operator do a route from Tana Bru to Rovaniemi (Mon, Thur, Fri and Sat - http://www.eskelisen-lapinlinjat.com/en/index.php?os=7), but as schedule for next winter isn't out yet you'll have to wait and see if they will run it then as well. It departs at 3:30am. The latest you can get to Tana Bru from Kirkenes seem to be at 6:00pm (boreal.no/ruter/520a-tana-bru-kirkenes-artic…), departing Kirkenes at 3:00pm, so so 9.5 hours at Tana Bru.
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