If LotR were translated into, say, modern Greek, would it be appropriate for the language of the Rohirrim to remain Anglo-Saxon? I think that Tolkien's comments in Appendix F prove that it would be much more appropriate to translate it into a more ancient form of Greek. Thus, the Anglo-Saxon-ness of the Rohirrim would be lost to a Greek reader. Tolkien made it clear that the language of the Rohirrim should appear to the reader to be in a more ancient form of their own language, so such changes in a translation would be acceptible.

: Other parallels between the two peoples are plentiful:

: Both have:

: Domestic architechture based on timber, though both can use stone (Hornburg - A-S churches, repairs/additions to Roman fortifications).

This is perhaps more an influence of their land than of their culture. Trees were plentiful and stone was not. Yet they were in control of remnants of the great stone-work of the Numenoreans (more on this in the quote at the end).

: Have codes of honour stressing personal bravery and faithfulness to a lord and hospitality to strangers.

This is a fairly universal characteristic of civilized societies.

: Give names to weapons and invest them with moral and temperamental characteristics.

: Bury dead leaders in earthen mounds.

These things are also done by their Dunadan neighbors. Tolkien said that they were under the cultural influence of Gondor. Gondor also did these things. Besides, these are, again, fairly common practices and are circumstancial evidence at best.

A footnote in Appendix F II directly addresses the relationship between the Rihirrim and Anglo-Saxon cultures:

This 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 had once been part of its domain.