Pretty much all cavalry that has ever existed favours fighting in open land to trees.
Yup. By their very nature, horses are animals adapted to open terrain. I pretty much grew up on horseback and riding through woods at anything above walking pace isn't something you want to do. You'd run all sorts of risks (your horse tripping over tree-roots, the rider getting knocked off the horse by running into branches, etc). I can't even imagine what it would be like to fight on horseback under these conditions. Your advantage of speed and mobility is completely gone in a forest as is your ability to maintain unit cohesion (say, to mount a charge).
Pretty much all cavalry always fought offensively, not defensively. Roman cavalry were only considered auxiliary troops, used mostly for "harassment".
Medieval Knights charged enemy infantry formations to break them up.
I can't think of a cavalry unit whose main purpose was to hold and defend territory. Why would you need a horse on defense anyway? It would only get in the way and/or panic and run away. And a trained cavalry horse isn't something you want to "throw away" - they're expensive to breed and train and their training takes time. The main strength of cavalry is high mobility on the battlefield. Dismounted cavalry are just worse foot-soldiers (since they're trained to fight from horseback, not on their own feet).
And all that can also be applied to the cavalry's successors in modern times (tanks). You don't use tanks to conquer territory, but rather to mount fast attacks and to drive the enemy from their positions. To *hold* whatever territory the tanks charged through, you still need infantry.
So I find the idea that cavalry is now able to fortify not just problematic but plain wrong.