How often exactly? I really have a problem understanding the campaign script at this point as the comments seem to talk a completely different language than the code.

What the code says is you need to win 2/3/4 battles against cav and the horse counter will increase to level 1/2/3 respectively. The same for gunpowder only without the last level.

So is it correct that you only need to win three battles against a larger army (i.e. with gunpowder and cavalry) to get all the goodies?