Did the early English ('Anglo-Saxons') ride horses? Evidence comes from both documentary and archaeological sources.
Several mentions in Bede's Ecclesiastical History, written in 731, indicate that riding horses was considered to be normal for royalty and bishops:
..[The chief priest] asked the king to give him arms and a stallion - for hitherto it had not been lawful for the chief priest to carry arms or to ride anything but a mare - and thus equipped he set out to destroy the idols. Girded with a sword and with a spear in his hand, he mounted the king's stallion ."
--Bede, Book II, Ch. 13
whether in battle or on a peaceful progress on horseback through city, town and countryside, the royal standard was always borne in front of him.
--Bede, Book II, Ch. 16.
[King Oswin] had given Bishop Aidan a very fine horse, in order that he could ride whenever he had to cross a river or undertake any difficult or urgent journey, although the bishop ordinarily travelled on foot. Not long afterwards, when a poor man met the bishop and asked for alms, the bishop immediately dismounted and ordered the horse, with all its royal trappings, to be given to the beggar [ ]
When this action came to the king's ears, he asked the bishop "My lord bishop, why did you give away the royal horse which was necessary for your own use? Have we not many less valuable horses or other belongings which would have been good enough for beggars, without giving away a horse that I had specially selected for your personal use?"
--Bede, Book III, Ch. 14
In the poem Beowulf, the coastguard who challenges Beowulf and his followers when they first arrive in Hrothgar's kingdom is mounted on a horse:
Hrothgar's thane, when his horse had picked
Its way down to the shore, shook his spear
Fiercely at arm's length, framed the challenge
--Beowulf, translated by Michael Alexander
War-horses are among the gifts given by Hrothgar to Beowulf for the slaying of Grendel:
The king the ordered eight war-horses
With glancing bridles to be brought within walls
--Beowulf, translated by Michael Alexander
According to the Life of Wilfrid, King Ecgfrith of Northumbria and his army of horsemen (equitatus exercitus) won an important battle against the Picts in 672 (Halsall 2003, citing Eddius Stephanus' Life of Wilfrid).
Horse bones occasionally turn up as grave-goods in early English cremation burials. For example, the cremation burials in Mounds 3 and 4 at Sutton Hoo both included pieces of horse bone (Carver 1998). Such bones clearly confirm that horses were present in early England, but cannot show what they were used for. They could indicate that horses were ridden, used to pull vehicles, eaten, or any combination thereof.
Confirmation that horses were ridden and were associated with the warrior class comes from three spectacular burials discovered in East Anglia. Mound 17 at Sutton Hoo, the only grave mound at Sutton Hoo to be discovered intact besides the famous ship burial, was excavated in 1991 and found to contain the body of a young man buried with a sword, two spears, a shield and various other items, and the body of a horse complete with bridle and reins. (More details in a separate article). The horse was part skeleton and part sand-body*, and sufficiently well preserved to show that it had been a thick-set male about five or six years old and standing about 14 hands tall.
Two other inhumation burials, each containing a man buried with weapons and a horse, were excavated at RAF Lakenheath in 1997 and 1999. The horse in the 1997 burial was also about 14 hands, and was reconstructed (along with his rider) for a BBC documentary. The burial was dated to around 550 AD (Lakenhealth Alumni Resources). The second Lakenheath horse was a little smaller and slighter, standing about 13 hands and aged about eight or nine years, and also dated to the sixth century (British Archaeology 1999;50).
Bede's story about the chief priest indicates that (a) the king rode a stallion; (b) the chief priest was clearly a capable rider, since he was able to ride and manage it; (c) there was a rule about the type of animal a chief priest could ride, which implies that he was expected to ride. Now, Bede's account was written down a century after the event and may or may not be an accurate reflection of real happenings - though I would hesitate to claim that we know more than Bede did about his country's recent history. It does demonstrate that in the eighth century Bede, and/or his source, thought that kings and priests rode horses in the seventh.
Similarly, Bede's story about King Oswin and Bishop Aidan, which takes place some time in the 640s, shows clearly that the king owned and rode horses, expected a bishop to do likewise, and considered a horse to be an important and valuable gift. The Beowulf poet, and presumably the poem's audience, also considered war-horses to be a suitable gift for a high-ranking warrior.
The mounted coastguard in Beowulf indicates that it was expected that at least some soldiers would ride in the course of carrying out their duties. The explicit reference to Ecgfrith's army as "horsemen" suggests that quite large bodies of mounted warriors could be assembled for campaigns in distant territories (Ecgfrith's army was invading Pictland, the area north of the Forth-Clyde valleys in modern Scotland). Whether they fought on horseback as cavalry, or were 'mounted infantry' who rode to battle and then dismounted to fight, or both, is a moot point, and a subject for another post.
The horse burials from East Anglia support the documentary evidence that at least some warriors owned and rode horses, and also give us an idea of what such horses might have looked like. All three were quite small, and would be considered ponies by modern standards (a pony is defined as a horse smaller than 14.2 hands). They must have been quite strong and sturdy to carry the weight of an adult man and his equipment, which is consistent with the Sutton Hoo horse being described as "thick-set".
Perhaps they resembled some of the sturdy British ponies still around today, such as the Fell Pony or the Highland Pony, also called a garron. These breeds are about the same size as the horses in the burials. They have been used for centuries in the uplands of England and Scotland, both for riding and for carrying heavy loads over long distances. Fell ponies heaved ore over the mountains from the Lake District mines, for example, and Highland ponies are still used today on some estates to carry the stags down after a successful stalk. When trying to imagine what an English warrior's horse might have looked like in the seventh century, I should think one could do a lot worse than start with the Fell Pony.
So, I think we can be fairly sure that the answer to the question, "Did the early English ride horses?" is "Yes", at least for the military and religious elite. To what extent this applied to the rest of society is a different, and trickier, question.
Bede, Ecclesiastical History of the English People, Translated by Leo Sherley-Price, Penguin, 1990, ISBN 0-14-044565-X.
Beowulf, translated by Michael Alexander. Penguin, 1973, ISBN 0-14-044268-5
British Archaeology 1999; Issue 50, web page (scroll down).
Carver M. Sutton Hoo: Burial ground of kings? British Museum Press, 1998, ISBN 0-7141-0591-0.
Halsall, Guy. Warfare and society in the barbarian West, 450-900. Routledge, 2003, ISBN 0415239397.
Lakenheath Alumni Resources, web page.
* Sand bodies were a feature of the 1990s excavation at Sutton Hoo. The acid sandy soil of the site sometimes interacts with a decaying body to leave a fragile crusty surface outlining the original surface of the body. These can be rather macabre, reminiscent of the plaster casts of the bodies at Pompeii. See Martin Carver's book for pictures; this photo on Flickr gives an idea.