Horses lag/shutter really much when playing on slower servers

When a 1.6 preview server is being hosted on slower servers, those with less CPU or RAM, horses tends to lag a lot. They sort of shutter when you ride them, making the ride unpleasant.
When playing single player, or on servers that have more CPU, the ride is oftenly less laggy, or no lag at all.

My guess is that the horse positioning and moving is done by the server, unlike when a player moves, which seems to be done by the client. Wouldn't it be less laggy if the horse moving would be calculated by the player that rides the horse?