The definition of
Scandinavian is as difficult as defining what
Scandinavia is. We have (at least) three criteria to consider here,
viz.,
language,
culture, and
history/
politics.
Linguistically Scandinavia, and hence, a Scandinavian, can only logically be Denmark, Norway, Sweden, Iceland and the Faroe Islands as they all speak Scandinavian langauges. Finnish, on the other hand, is of a different linguistic branch, i.e., the Finno-Ugric group of languages (Estonian, Finnish, and Hungarian).
The cultural perspective is the hardest to look from. Can we say, for example, that a Finn is no less Scandinavan than a Dane or a Swede or a Norwegian? This is very difficult. It has to do with what we perceive as the fringes of "Scandinavia"... We would include Iceland and the Faroes, but then do we include Greenland? -- although the Inuit are not ethnically or culturally really Scandinavian the country is a Danish colony and they do share some kind of common Scandinavian experience. I find this "experience" hard to put into words, but anyone who has been to any one of the Norden countries, or maybe someone who has read their literature, or even heard Songs from the Cold Seas will know what I am getting at here...
From a Historical or Political perspective, however, Scandinavia(n) has to be considered to be inclusive of all the "Norden" countries and cultures:
Denmark, the Faroe Islands, Finland, Greenland, Iceland, Norway, Sweden
See also the Scandinavian Metanode.