At university I remember being taught that a nose twitch is a great way of subduing a horse for treatments such as stomach tubing. Also taught was the possibility of using an ear twitch or a skin pinch. They were not as effective but thought to possibly help in some horses. At the time I remember (although it is long ago!) that all the modes of twitching were thought to do the same thing: increase endorphins and relax a horse so that a mildly invasive procedure could be performed without sedation.
In my experience in the field, I have seen many owners ear twitch their horses. I have never found it to be useful and observed that every horse would try to pull away, either before the ear was grasped, immediately as the ear was held and twisted and/or during the hold. Horses often pull away from a nose twitch but after a short period of time I often saw the nose twitch lead to a horse looking like it was sleepy: with floppy lips and a bowed head. With the ear twitch I never saw that response.
A recent study has shown that an ear twitch induces a fear response both behaviourally and physiologically in horses. The nose twitch can reduce physiological and behavioural signs of fear if used for less than 5 minutes but longer use can be associated with the effect wearing off and fear being experienced. If twitching horses the ear twitch should not be used and nose twitching should only be used for short periods.