Where are you from? If you're an EU citizen then that's fine, but anywhere outside of the EU you won't be able to get a work permit and residency in the EU. (Had you been a research scientist or similar, then maybe, but tattoo artists aren't exactly in huge demand in Finland.)
And what exactly do you mean 'would money be an issue'? Yes, you do need money to live anywhere, including in Finland; the world does not owe you a living. For starters, you need a place to live, and it might be nice to occasionally eat something also, and perhaps even buy some clothes (it's pretty cold in Finland, I can tell you from years of experience of living there). Tattooing isn't exactly a get-rich-quick occupation, so you could well struggle just to make ends meet.
And as for the language issue, perhaps you're not aware that Finnish is considered among the top-3 most difficult languages in the world? I have a friend who is a linguist and tried for several years to learn Finnish, and barely got out of the starting blocks. So by all means give it a go, but don't expect to be fluent any time soon. (Swedish, incidentally, would be a far easier choice.)
If you're not an EU citizen then moving with a profession like a tattoo artist could be hard. You should learn the language, but it's not as hard as some people say. I had a exchange student for a year living in my family and she could speak understandable finnish at the end of the year. Everyone does understand english (If not including old people) If you'd live in the south then summer is pretty warm and the winter isn't that cold either. It's windy though.
It is essential in Finland to speak Finnish well, otherwise how can people tell you what they want their tattoos to be like? Finnish is a very difficult language, much tougher than any language you have previously attempted.
Money will be an issue - to get a work visa, you will need to prove you have the money to start a business that will employ people.
Pro: Finland has a wonderful summer, beautiful lakes and wild swimming everywhere, lots of excellent campsites in beautiful locations with superb facilities.
Con: Finland has a very, very hard winter - long periods of -20C or -30C.
How will you get a visa?