Are the Rohirrim Anglo-Saxons? I agree that they are not; they are an invention of Tolkien's. Were they influenced by Tolkien's knowledge of the Anglo-Saxons? I think they undoubtedly were.

The bottom line is language, whatever the origin of Tolkien's use of a version of Anglo-Saxon for the speech of the Rohirrim (archaic English compared to modern = an archaic variant of Adunaic to Westron) on the page the words are Old English and this will unavoidably affect how the reader views the speakers.

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).

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

Have a heroic poetry which is based on alliteration and the use of a caesura (pause) in the middle of a line.

Have a penchant for using by-words - such as whale-road for sea or war-board for shield.

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

Bury dead leaders in earthen mounds.

These are just some of the more immediately obvious parallels.

Some of the differences you quote are not quite as clear-cut as you might like. Much of Rohan was lowland, though the major fortified sites were for obvious reasons constructed in the highlands. Also some of the Anglo-Saxon peoples were settled in highland - try telling a Pecsaete or Elmetsaete that the high Pennines were lowlands, or a Wreocensaete that the Wrekin hills were mere molehills ;)

Also, judging from pictographic evidence, the Northumbrian Anglo-Saxon army defeated by the Picts at Nechtansmere in the 7th century was composed wholly of cavalry.

The Anglo-Saxons, as opposed to the Angles and Saxons, were not particularly effective seafarers. Once the Anglo-Saxon kingdoms had arose in Britain any inheritance from the Saxon pirates who preyed on the Late Romans of Britain and Gaul seems to have been quickly lost as most sea traffic in Northwestern Europe was carried on by the Frisians. The eventual English response to Viking sea power was a rather artificial one spawned by the genius of Alfred the Great, and not drawn from a strong sea-faring tradition previously exhibited by the English peoples themselves.