Alright I can get why you might not use horseback bows, but swords instead of spears (yes, spear, not lance. that thing is horribly slow)? That's just wanting to gimp yourself. Spears are awesome, always thurst, deal tons of damage and strike really fast. My prefered this far is the balanced long awlpike, but have to try the light lance yet.
Currently I'm trying the heavy hafted mace and finding it awesome. Polearm-reach with blunt damage and always thrusts on horseback? Sign me in. The only downside is the reduced damage, but it doesn't stop it from knocking out tier 2+ archers in one good hit.