Flew to lapland (Swedish side though) last year.
Dublin --> Stockholm with Aer Lingus
Stockholm --> Kiruna (return from Lulea) with I think Norwegian or somesuch.
all in all less than 350 per person return. Was happy enough with that.
Not sure how I would tackle Finland. Potentially Ryanair to Tampere and than again Norwegian to go further. Stockholm however seems to be a good hub for going further North, as was Oslo.
I went through London with Thompson a few years back. Booked as a skiing holiday without ski passes etc rather than as a Santa holiday and it was much less expensive. Was able to much all the Santa/reindeer trips as extras.
Tripadviser has a really good forum on Lapland holidays with loads of advice on how to cut costs. Ryanair to Tampere and overnight train to the Arctic circle was popular.