@Ziegenpeter
I propose this first...

Horse is not a cheap animal.... and I don't have any...

But if we want to test this, I have an Idea... (no, this test won't kill your horse in question)
1. Collect some old plastic toy swords from your neighbourhood about two dozen or three. Mount them on some long 5 m bamboo rods, or stick.
2. Ride your horse into a large open plain (or a really big backyard)
3. Give each "toy sarissa" to your friends, and try to form a phalanx (give them EB screenshots).
4. Now ride your horse slowly to these bristling wall of "toy sarrisa"
5. See if your horse want to going deeper into the spearwall or not... I'll wait your test result...
But, nobody want to use my suggestion and do that experiment...