I don't teach formal lessons - I teach friends and family and also teach at pony club.
When teaching friends it is normally while out on a ride as we go - So yes I am on my horse. My horse is better educated than most they ride so I will often show them something, then put them up on my horse to try it out on a horse who knows it - They seem to like this method.
At pony club I am often on Latte while teaching and will just be sitting still or walking around - Both things that are greatly beneficial to a young horse. I don't think it effects the teaching at all.