I'll just note that while we are reading about the actual horse-culture and arms of the Rohirrim, with the language we are not actually looking at the true language of the Horse-lords. Anglo-saxon is a translated language, just as Modern English translates the Common Speech.
Is Anglo-saxon anything like the actual tongue of the Rohirrim, in any sense or measure? Historically the Rohirrim spoke a language that preceded Anglo-saxon by many years, and for evidence we only have a few words in the genuine language of the Rohirrim (counting those published by the author himself in Appendix F). For examples: trahan 'burrow' kastu 'mathom' and kûd-dûkan 'hole-dweller'
And we can see that Old English holbytla (used in translation), at least, sounds nothing like the genuine word the Rohirrim used, in kûd-dûkan. In Appendix F Tolkien even noted...
'The linguistic procedure does not imply that the Rohirrim closely resembled the ancient English otherwise, in culture or art, in weapons or modes of warfare, except in a general way due to their circumstances: a simpler and more primitive people living in contact with a higher and more venerable culture, and occupying lands that once had been part of its domain.'
The Return of the King, Appendix F, On Translation
That said we have Tom Shippey, for example, 'disagreeing' with JRRT about that, or at least arguing, in part, that the Rohirrim are based on the Anglo-saxons of legend and poetry. But what about the actual tongue? From Letters...
'Since the Rohirrim are represented as recent comers out of the North, and users of an archaic Mannish language relatively untouched by the influence of Eldarin, I have turned their names into forms like (but not identical with) Old English. (...)
The Rohirrim no doubt (as our ancient English ancestors in a similar state of culture and society) spoke, at least their own tongue, with a slower tempo and more sonorous articulation, than modern 'urbans'.
This is the only reference I could find so far with 'slow' in it (given the description noted below), but this seems to be about a manner of speaking. The only other evidence I recall at the moment is that Aragorn chants softly in a 'slow tongue' which then has a strong music in it. And:
'That, I guess, is the language of the Rohirrim,' said Legolas; 'for it is like to this land itself; rich and rolling in part, and else hard and stern as the mountains.'
Hmm. I checked Hammond and Scull's reference to Anglo-saxon (in their amazing Reader's Guide) and could not find them quoting Tolkien describing Old English, or (so far) any Primary World language, in a similar way. Not that he never did, but I think this would be notable, if so.
And even if we say Sindarin, for example, is 'like' Welsh in some way or measure, I'm not sure what that means beyond the external fact that the general phonology and some grammar of Welsh inspired Sindarin. And obviously Tolkien did not use Welsh to translate Sindarin.
With Old English we are really looking at a much later language that only arose in northern Europe well after the Third Age had passed.
Old from our perspective, Anglo-Saxon is an unknown language of the future to Frodo and the Elves, and it was employed by the modern 'translator' (Tolkien playing the part of translator) to translate some ancient, actual language of the Rohirrim (which must be related to the languages of Frodo's day), just like we are looking at Modern English to translate Westron.
This was done not because the original language was necessarily like its translated language, but to try to illustrate a relationship between the languages of Frodo's day. In theory, within the conceit, Tolkien the translator is looking at various languages in the Red Book or copies of it: it's not all one language, and the translation procedure itself is not all Modern English either.
Of course Modern English is the one chosen for the Common Speech so English readers can read it. Obviously if one speaks only German, the Modern English version is again translated into German. German then essentially translates Westron; although Modern English intercedes as it must, as in real life there is no Common Speech version of the tale.
Erm... whatever all that means, or doesn't mean, in the context of this thread :)