Your mistake is to consider an election is a rational competition. It’s not. Not anymore, because medias make it impossible to know the truth. So it is more like a football match. People have the team they support, and for most nothing will change their mind because there’s too much propaganda. When almost everything is propaganda, you get to choose the reality you “prefer”.
So the point of the campaign is more about convincing people to vote in order to defeat the opposing team. Or to persuade the other team to concede.
Horse archers, or skirmishing units in general, are countered by archers or siege units. Unless the game is wildly unbalanced it always works.