I don't know of any other uses in literature, but owls are considered ill omens in quite a few mythologies and cultures. Owls are often seen as the messengers or companions of gods of death, or are associated with sorcery or evil, especially in African and American (north and south) cultures.
You may want to look at Mercedes Lackey's Hawkbrothers culture in her Valdemar series. They use birds-of-prey, including owls, as a sort of familiar. I can't remember her ever having them carry physical letters ever, but they could be used to transfer messages between scouts...
Perhaps it will give you some ideas of how to make your owls less Rowling-esque and more unique to your own story.
I know but in terms of direct magic-related influence? (Like association with witches, etc.)?
Just thinking because I'm working on transforming a fanfiction (except not really, it was a NaNoWriMo piece set in the HP universe on a different continent with no Rowling characters, just for consistency and to save time at the last minute). I'm trying to decide if I should get rid of all my owls (there aren't that many).
Well, I'm not sure if owls have ever been directly associated with witches and wizards, but owls themselves symbolize wisdom and clairvoyance. I'm sure long ago people believed they could view the future. The only other thing I can think of is 'familiars.' A familiar is basically an animal (usually a cat, but could be an owl) that acts like the witch's partner.
But the idea of owl messages is what Pakaku said. It was just a means of communication for the magical world.