It doesn't make much sense to look at the average population density of Finland. Homeless people don't really roam the empty countryside, they are in the cities, probably much like in the US too.
In areas of the USA with the average temperatures of Finland there isn't much (any?) homelessness either.
And your point is...?
I mean I guess culling the population to make the price of housing drop is one solution, but it's a bit strong don't you think?
The point is its easy to fix homelessness when land is cheap and building materials are cheap. It doesn't really help our problems in big American cities.