If you've read our "In a Nutshell" section, you know that this poem comes in right near the very end of Love's Labour's Lost. You should also know that some Spanish dude named Armado actually asks the king if two of the guys who performed the play-within-a-play can come out and sing the final songs of that play-within-a-play. The king, obviously, is cool with that request.
Sadly, however, we don't really know who actually sings these songs. Some people speculate about it, but that's really beside the real point, which is that the song is more important than who sings it, just as in the play itself, the wordplay and the puns and the games are all a little more important than what actually happens. Anyway since we don't know who for sure is speaking "Winter," we get to make some stuff up. Well, within reason, we get to. We can't say it's, like, Tom Cruise or anything.
Here's what we can tell about the speaker just based on the details we have in "Winter." He's clearly good at painting a verbal picture—he gives us a succinct series of images that really give us a great idea of village life during the winter (frozen milk in a pail, a guy carrying logs, some "greasy" woman stirring a pot, an owl getting ready to hunt).
Speaking of villages, clearly our speaker is quite familiar with village, or rather, rural life. The use of the present tense throughout the poem ("blows," "bears," "nightly sings") suggests that our speaker is on the scene, reporting the action. It's either that, or he's just recently come from the scene and is giving us a play-by-play through his eyes, kind of like a journalist might do.
He may have just come from this scene because, just maybe, he's originally from there. This is a pretty good guess because, well, in Love's Labour's Lost, the guys who perform the play within a play, of which "Winter" is the concluding piece, are definitely lower class dudes—"rustics," if you will, less-educated, pastoral folk who, back in the day, often worked as entertainers for royalty and the like (the audience for this play-within-a-play, remember, is the king of Navarre, his nobles, a princess, and her attendants).