Azza, I would recommend against cold, simply from the extra clothes required, and specifically about what clothes to take. I start commuting as soon as the snow and ice is mostly gone and until it appears, but it has taken me a number of years to figure out what clothes work for a given temp. I would also add that riding in cold and rain where it's under 10c is particularly unpleasant and has its own issues of not getting chilled, especially the hands.

Of course you can figure it out, it's not impossible, just for an enjoyable trip I'm more inclined to avoid cold. I reckon it would be a lot easier for me to properly choose cold weather clothing for a trip just from the commuting experience and our climate, not as easy for you to do where you are.

Mind you, you are strong and in your 20s and not an old fart like me, so you'd muddle through pretty much anything and have an adventure....