As an under 16 you need to have a parent or guardian register as well. You register as a junior rider and the adult as a non jumping member. You then register the horse as (predictably!!) a horse rather than a pony. There are various new member discounts through membership of pony club or a riding club etc. As you quite rightly say you have to compete in horse classes - but you still do so as a junior rider until the end of the calendar year in which you turn 16.