It depends a lot how you go about that whole "learning Finnish" thing. I have not tried the tax payer leech route, so all I know of those classes is hear-say. My friends say, one learns English fast there. In the Finnish classes

If you have the monies to cover living in Finland AND paying for lessons, you can get far in those 3 months. I'd rather look at yksityisopetus.fi - not group courses, so the social interaction you have to get somewhere else. Also, it is the free market of course. But you may find those that think outside of the box.
The timing is a bit suboptimal for the "Santa's elf in Lapland" scenario, as they are hired about now (and a bit I guess). Even elves need to understand the locals

But in general, it is a good idea. Tourist-y areas may have opportunities for foreigners who 1) understand and speak enough Finnish 2) want to WORK and 3) are not too picky.
BTW, you may want to make your monies last as long as possible. Consider to NOT live in Helsinki. It is rather expensive. Even if you are Helsinki oriented, check costs etc. of public transportation from other places.
BTW2, life instruction beats Skype by far, in my experience. I am not quite sure yet why, my Skype teacher was awesome. And osmosis takes a while to work with this language, but does after some time. So, being here helps tremendously to learn it.