Couldn't seem to find an answer googling it.

If I buy the imperial edition but choose to play an Orc or something can I still ride the imperial horse?

AFAIK you can use your white horse mount regardless of what race character you pick

Any race can ride it.

My Bosmer enjoyed hers in the last beta

Will all characters be able to share the Imperial horse or any other purchased horse? Or does each character slotted need it's own horse?

Every character will need its own horse.