Besides training with weapons and horses what kind of exercises did they utilize? It seems logical to me that there would be some kind of calisthenics and perhaps even rudimentary weightlifting to keep match fit for war and tourney.
A prior discussion of medieval exercise in r/askhistorians can be found here.
De Re Militari was widely read through the Middle Ages, was reproduced in many editions. It recommended that military recruits run and jump regularly, swim in the summer months, march carrying weight, and labor such as chopping wood, carrying loads and crossing ditches. Also it recommends weapon practice by hitting a post with wooden weapons weighing twice that of proper battlefield weapons. Wiki.
The Konungs skuggsjá (Old Norse for "King's mirror"; Latin: Speculum regale) is a didactic text in Old Norse from around 1250. It addresses politics and morality as a source of education for a prince, specifically Magnus Lagabøte, or Magnus IV of Norway. Wiki.
One subject that it covers is the recommended forms of diversion for a king’s henchman.
Horseback combat training: practice “in heavy armour” and “press the foot firmly into the stirrup; keep your leg stiff and the heel a little lower than the toes, except when you have to guard against thrusts from the front; and practice sitting firmly with the thighs pressed close. Cover your chest and limbs carefully with a curved shield.”
Foot combat: “put on heavy armor; look up some fellow henchman/warrior who likes to drill with you and whom you know to be well trained to fight behind a shield or a buckler. Always bring heavy armor to this exercise, either chain mail or a thick gambison, and carry a heavy sword and a weighty shield or buckler in your hand. In this game you should strive to learn suitable thrusts and such counterstrokes as are good, necessary, and convenient. Learn precisely how to cover yourself with the shield, so that you may be able to guard well when you have to deal with a foeman.”
“If you feel that it is important to be well trained in these activities, go through the exercise twice a day, if it is convenient; but let no day pass, except holidays, without practicing this drill at least once; for it is counted proper for all kingsmen to master this art and, moreover, it must be mastered if it is to be of service.”
Training ambidexterity: “Formerly the custom was for all who wished to become expert in such arts and thoroughly proficient in war and chivalry to train both hands alike in the use of weapons. Strive after the same skill, if you find yourself gifted for it, inasmuch as those who are trained in that way are the most perfect in these activities and the most dangerous to their enemies.”
Trivia: in 1867 a military officer Otto Blom made a study of the various types of weapons, armor, and siege engines mentioned in the "King's mirror", and argued that it dated the work to the later thirteenth century.
A very nice article “Keeping Fit in Later Medieval England: Exercise for Man and Beast” focusing on 16th c can be found here.
Edit: some grammar corrections.