As stated in the title, if one of my character unlock a costume from the winter event, will my other characters on the same account get it unlocked as well?

With the exception of C-Store ships, almost everything new is per character now.

The tooltip for winter event clothing says 'common item', so I take that as an unbound item.

Can anyone confirm the coats aren't bound?

The costumes are character unlocks, not account unlocks.
The coats (and presumably other clothing items) once purchased come inside of a crate. The crate itself can be freely traded or sold, however upon opening it to receive the item inside, the prize become a character unlock.

Well that sucks