Warhorses are not retrainable, can't further train them, aswell as Heavy Warhorse.
Cannot get a Spirited or a Royal one too at all.
Skill progression for Heavy Horse Handling is waaay too slow.
you can still use 2-handed weapons while mounted, just need to take them in combat stance before bounting then mount up and enter combat stance.
Please work on mounted combat and lancing so next patch it works more properly.