My impression is that zombies don't have the capacity to use weapons (that is more of a skeleton thing) or gain many (if any) class benefits from their previous life (that is more a lich/dread knight/hecuva thing), but we don't have a zombie template so that is a "rulings not rules" area.
The zombie description does say that they'll use weapons if you give them to them, but won't pick them up off the ground unless you tell them to. Seems like more of a "lack of initiative" thing than a non-proficiency thing.
As DM, I wouldn't have a problem with someone giving a greatsword to a zombie but I'd look askance at a longbow or crossbow zombie. Too many moving parts. I'd probably just make that zombie start hitting things with the crossbow itself, like a club.