I'd say the initial attack was a ranged touch attack (you don't have to get past armor to lasso someone). If the attack hits, the target would be entangled. The target would probably get a Strength check (DC 23 for hemp rope, DC 24 for silk) or an Escape Artist check (opposed by Use Rope check, though the attacker would not get the +10 bonus for 'binding someone', as that bonus implies a careful, methodical approach to tying someone up).
Pulling someone off their feet would be a trip attack, though in this case I might give the attacker a +2 synergy bonus to the trip attempt if they have 5+ ranks in Use Rope. Tying the rope to a saddle is a simple Use Rope check, and then you could use the horse's bonuses (Large size, stable creature) on the trip attempt. Dragging someone you'd have to guess yourself, maybe something like 1d6 damage for every 20 feet on movement from the horse (not quite as bad as falling, but still painful).
But I'd treat the initial lassoing and any subsequent trip/drag attempt as separate attacks, which means that unless the attacker is high enough level to get multiple attacks in a round the defender will probably get at least one chance to slip out of the lasso before being dragged.
