While I know this is a personal preference, me and my father used to practice archery, and the shoulder quivers were extremely ackward for me to use. I only used a couple, but reaching over my shoulder to grab then was rather cumbersome and I felt silly doing it. I'm guessing that there are people who associate that with the "right" way because it's seen in movies and whatnot.
In my opinion it's faster to stick them in the ground, or in one of those things on the floor that don't leave holes, and pull them out. To run in, a bow mounted quiver is best, but is also a bit tricky to draw quickly. You really can't run or jump with shoulder or side quivers, not any I've seen at least.
Not to mention, the added bulkiness of any armor would make it even more difficult, if not impossible to reach it.
But since it's a game, and if nothing else the bowstring would fail at the constant inclement weather, we can just safely assume that it doesn't matter? I don't think a side quiver would hurt anything.