The tennis-racket-like snowshoes you probably think of when people say 'snow shoes' is a native American invention.

Scandinavia did not use snow shoes to the same extent; we used skis. But there was a kind of snow shoe, called trugor/truger/trygor/trögor (Old Norse þrjúgr) also named skarbågar/skarbuger . These were used for horses in snow and marshy land and could look like this but also be solid blocks as seen in action here. Human models could also look like this.Trugor is also the name for the similar part at the end of a ski pole.

These were not so common though. As this Swedish article on snow shoes states: "It is likely unknown to many of this essay's readers, that "snow shoes" reminiscent of the indians', have also been used for centuries in the Nordic countries." - and this is an article from 1929 and in the annual of the Swedish association for the promotion of skiing (Friluftsfrämjandet). So they'd fallen into obscurity here even before urbanization and snowmobiles.

Snow shoes require no particular practice or skill to use, so it's not so surprising snowshoes they'd be adopted instead of skis among North American settlers coming from cultures with no tradition of skiing. (since a long time it's been speculated that Scandinavians themselves learned it from the Sami)