Hard riding no saddles or stirrups

[Tiberius Martius]

Sure, but charging directly into formed up heavy infantry was not the standard practice of the Medieval period either, or not a very successful one, so I'm led to believe. I can't agree that Stirrups made all the difference, but that remains something of a debating point. 'The Great Stirrup Controversy' touches upon this:

http://scholar.chem.nyu.edu/tekpages/stirrups.html

Stirrups are no doubt an advantage, but how much of an advantage it is difficult to say at this time with any real certainty.

Notice why I mentioned several possible reasons including horse size and stature and the tactics of the time. I used that as an example, watching hollywood movies does not always give an accurate depiction of the warfare of the time and this is the point I'm making. Stirrups did not make all the difference and I never said that they did. I said they were part of the reason and then included other possible reasons as well, including the lack of number of cavalrymen, their status in society and horse size and tactics.