I discovered this shortly after I received [Preserved Holly] from a Winter Veil quest. It allows you to be mounted and still have your pet out. Unfortunately it's kind of useless b/c the pet attacks are grey'd out, and if you aggro a mob, your pet wont fight it if its on defensive mode.
1. Complete the reindeer quest by finding him in searing gorge or tanaris (Pick up Q in a Major city)
2. Turn in Q, mount up, and use the preserved holly -- pet should appear as if it were just summoned.
Happy Holidays!