How much has Finland's culture been influenced by the Vikings, historically?

This is an interesting question, though huge in scope. First, there's the problem of defining "influence by vikings". Historically, Finland has been deeply intertwined with nordic cultural influence, by being a part of Sweden for over 600 years and by having an minority of ethnic swedish population.

If you specifically mean norse, "go on a viking" scandinavians, it's much harder to answer, since neither culture was literate enough to write historical records. There's a prevailence in the Finnish language of old norse/protogermanic loanwords, which suggests that they've been adopted long before swedish hegemony.

There's also the prevailence of the ethnic swedish minority of Finland, though the age of these settlements are controversial. There's either the view that these settlements show a continutiy of nordic influence since at least the iron age, or that they're a product of early medieval swedish colonization. I'm not read up on this debate, but a quick look at the wiki page seems to point to the latter view as being adopted in both finnish and swedish academia at the moment.

I think you also might get some answers from this old thread about viking raids in Finland: http://www.reddit.com/r/AskHistorians/comments/1ohsxz/why_didnt_norsemen_vikings_conquer_finland/