It's remotely plausible (though unlikely) that some group of inuits could wind up in Iceland or, possibly, even the Faroes. It's less likely that they could get to Ireland, Scotland, Norway, or England.
In any case, if they did, they might land and trade fish for goods (if they're not killed). However, they'd likely conclude that it wasn't worth the arduous journey and not good back.
The trip might span legends of a "strange land with people the color of snow faraway to the East," but even those wouldn't likely spread too far.
Assuming this West -> East "discovery" was made first, the biggest impact might have been in encouraging the Vikings and such to explore West earlier since they know SOMETHING is over there. So, you might have Viking colonies earlier. If word gets out to Europe at large, perhaps Columbus considers sailing somewhat more Northerly and lands near Maine or some such. If THAT happened, that would change the European impression of likely wealth over there, perhaps slowing or refocusing European exploration/colonization.
Under what, if any, plausible circumstances can you imagine the Native Americans discovering Europe instead of the other way around?