This is actually a good question. Basically, from what I've seen, if you spawn on a donkey with a weapon equipped, that cannot be used on horseback, you will have it equipped and be able to use it. But if you switch weapons you won't be able to equip it again while on the donkey.
I was on NA1 earlier and this actually came up as a viable question as there was a certain archer using a Rus Bow while riding a donkey (something that is not usable on horseback) and this caused victory. A few people in server, myself included brought this up as Eyebeat was on at the time, but nothing was really said on the matter and they were allowed to continue doing so. Just curious to have it clarified.