It's unlikely that anyone ran for reasons other than urgency or childhood exuberance as the Old English word for running and riding (ærn) is the same, suggesting that one of these pursuits was underdeveloped (spoiler alert: it was probably running as there's 16 words for different types or use of horse).

Similarly the word for "a way fit for running on" (ærning), also means "a broad road" which is presumably fit for riding on. Obviously this system isn't conclusive, but it can give us a wee glance at the 'size' a concept occupied within a a particular culture.

However, I’ll back up the assertion that hunting formed the bedrock of nobility’s workout regime.

Hunting and hawking were the past-times of choice for the nobility in Anglo-Saxon and Anglo-Norman England, this was both physically exerting but also lead to a prominent diet of deer, fowl and other game – so it can be argued that it impacted on their health twice over.

Hawking was taken incredibly seriously and training of hawks was seen as an important part of a young nobleman’s education. Alfred the Great (849-889 CE) was considered extremely proficient and is reported to have written a treatise on the subject, although there’s no evidence of it, and Edward the Confessor (1005-1066) dedicated a huge volume of his leisure time to it.

Alexander Bicknell writes in The Life of Alfred the Great: King of the Anglo-Saxons, that:

The Saxons from their German ancestors holding hunting in great esteem, as it contributed to health, enured them to hardiness, and rendered dangers (their pursuit being confined to wild and noxious beasts) familiar to them.

In this delightful text from 1777, he expands further on the benefits of the hunt:

The education of a mere military age principally consisted in those bodily exercises, which taught the pupil an expertness in the management of his arms, and prepared him for the gracefuller discharge of the duties of war […] these were the principal objects of active life.

John Thrupp's 1862 volume The Anglo-Saxon Home: A History of the Domestic Institutions and Customs of England, from the Fifth to the Eleventh Century posits rowing as a keen pursuit of the Anglo-Saxon nobility, recalling the 973 coronation of Edgar the Peaceful (943-975) in Bath where six British kings (massaged into eight by the Anglo-Saxon Chronicle and, as a result, by Thrupp) swore allegiance, including the King of Scots and the King of Strathclyde:

As the Anglo-Saxons were constantly on the water, they naturally put a high value on skill in boating. The able use of an oar was a source of pride to men of the highest rank. Eight kings condescended to row Edgar from Westchester to the church of St John while the fiery monarch sat and steered.

The sheer effort required in rowing suggests both a certain level of physical fitness and practice from the monarchs present. Further Northeast, swimming seems to have been a popular activity with Viking Age rulers:

To be a powerful swimmer was deemed by a Danish warrior an almost indispensable accomplishment. Olaf Frygesson, the famous king of the Northmen, was the most powerful swimmer of his time… in the “brags” in which the Danes indulged at their convivial meetings, wonderful and indeed impossible feats of swimming were told.

Olaf Frygesson, is most likely Olaf Tryggvason (960s – 1000), who is one of the many Norse rulers to plague the British coastline and be attributed swimming prowess. Thrupp also claims that the Danes loved ice-skating, providing some glorious inspiration for this year's Christmas Yule cards:

Tales of the wonderful skill displayed in it are as incredible as their accounts of their swimming. They not only, if we might believe them, skated over lakes and frozen seas with the rapidity of the flight of angels, but skated up to the summit of the highest mountains, and came down again with the help of an alpen-stock at a far greater pace.

Additional source: The Anglo-Saxon World by Nicholas Higham and M. J. Ryan, An Anglo-Saxon dictionary by T.N. Toller and Early British swimming, 55 BC - AD 1719 by Nicholas Orme

I have never come across any literature pointing to nobles jogging in particular, but nobles did hunt in the middle ages; while they didn't hunt specifically to get exercise, it is of course a physically demanding activity nevertheless. I'm going to use an unlikely source: Marie de France's "Lanval." In short (for context), the fairy mistress is dressed in regal clothing made of extravagant silk and is described as having just enormous amounts of wealth; she's a noblewoman. She is riding a horse with a raven and a greyhound. All of these are hunting animals. Nobles hunted on horses, using greyhounds and ravens to go after prey. The noblewoman hunts not to exercise, but because it's a noble activity. This way she could still separate herself from lower classes who could not afford to hunt (land was expensive). This was written by Marie de France around 1200, a time during which there was a large emphasis on nobles separating themselves from lower classes; this has almost always been historically true and certainly continues into the early modern period. While I'm not even sure if this is an acceptable source as it's not historical, I hope the insight is useful.