Yes, I've used the "hide in the forest" approach to good effect against the Golden Horde and a few other armies myself. In the woods cavalry get slaughtered, they are also weak in a stand up fight once the charge finishes, but if used well, cavalry can turn battles better than any other unit types in my experience.

In order to be prepared for anything your opponent may throw at you, you need the flexibility of a balanced force - no question. Cavalry does have the advantage of being able to dismount though, and while it may not be much better in some case, dismounting your Knights into Foot Knights means that even in trees you have a powerful unit.

I'd never use an all cavalry force, or even a very heavy one. Most often 4 or so units of mixed cavalry is plenty. A couple of heavy cavalry like Feudal, Royal or Chivalric Knights (even Mounted Sergeants in a pinch) with 1-2 fast light cavalry such as Spanish Jinettes or Steppe Cavalry is generally more than enough.

It's not that cavalry can win the day all by themselves, but they do seem to deliver the key blows most of the time. Delivering rear and flank attacks to key enemy units to break them, running down archers to trigger routs or target generals and harrassing fleeing troops to rack up extra kills and prevent regrouping are all things that cavalry excell at. Add to this the fact that they can disengage from combat more easily that other units given their speed and I don't know what I'd do without them.