The reason why you can only take a partial action if doing a melee attack, is basically the same reason why you only get a partial action if you are moving more than 5' on foot. Essentially it take too much time to "get to" the target for you to unleash a full volley of blows. Again it's another simplification.
The reason you can get a full attack in while doing archery is that unlike a melee attack, you can effectively be shooting during the entire time you are riding. As opposed to a melee attack where you have to wait until you get to the target and then probably are moving past it.
IRL a good rider with a familiar mount is supposed to be able to control the mount using just pressure from the legs and other subtle indications. So its not really taking an action.
The Drawing weapon example is shown as taking a partial action, because drawing a weapon takes a partial action, it has nothing to do with the char being on a horse. Any action that you perform on a mount is still going to take the same amount of time it would take you on foot at least.
So it's not "controlling the horse" that causes you to only get the partial action, its the time it takes to get to the target. The horse's movement essentially takes place separately from what ever actions you are doing. So, yes you can take your full complement of standard actions, though there may be penalties if the mount is taking more than a standard move. There are for both mounted combat and archery.