I'm afraid that I'm more of a history geek, particularly about military history, than is Professor Bainbridge. For the moment, leave aside that the strategy and tactics of The Lord of the Rings (book or Jackson's film, for different reasons) reflect considerable ignorance of what it takes to actually support a warfighting force, even for a short campaign. For example, if one does the math, based upon preindustrial North European agricultural productivity, and allows for the losses at Helm's Deep, Rohan's population must have been somewhere between that of England and France in the 12th century to send forth 6,000 mounted warriors with hope for more who didn't show—and neither the books nor the films support that great a population density. We'll also leave aside the tactical and strategic ineptness of the leaders on both sides—because, with very few exceptions, that is realistic. If Sauron or Saruman had any sophistication at all, they would have just beseiged their targets instead of storming them; Theoden would not have charged downhill into a force that had clearly already broken into the city; and so on.
I think the most logical antecedant for Rohan, though, is the pre-Muscovite Finns and Swedes. One of the great virtues of Eisenstein's Aleksandr Nevsky—aside from what is quite possibly the greatest score ever purpose-written for a film—is that there is substantial historical evidence behind it. The Battle on the Ice most probably did occur very much the way it was filmed; the "Viking" invaders were Finns and Swedes, historically; and virtually everything else fits the Rohirrim culture, except the numbers involved.
As a lesson in numbers, consider this: The English army at Agincourt (St. Crispin's Day, 1415) numbered between 4,500 and 5,500 total, with less than a thousand "men at arms" (think Gondor's footsoldiers). It was opposed by a French force of between 8,500 and 14,000 (some estimates go much higher, but the records of the baggage trains don't support them), about one-third mounted and virtually all foot close to the "man at arms" standard. Those two forces represented respectively 60-70% of the field military forces of those nations at that time.
To quote another of my favorite (underappreciated) movies:
You've got another scene. I'll write you another scene. It won't make a damned bit of difference. The studio'll cut 'em all out like they do everything else. All you'll have left is a bunch of swell battle scenes—which, when I was back there last time, they said looked just terrific.
In a nutshell, that's what's wrong with Jackson's The Return of the King, which I found a disappointment. Given the competition, it's still a comparatively very good film—but it's not nearly what it could have been.