The horses bred by the most effective mounted archers were used to
grazing as opposed to horses that needed grains to feed. Thus the
armies of the Huns, Magyars, Mongols, etc. did not need carts to carry
food for their horses, making them more mobile than other armies.
Moreover, European archers used crossbows, which were very slow to
reload (2-3 shots a minute as opposed to 15-20 shots) and impossible
to use while riding a horse.
That’s really interesting information, about the high energy balls of feed. Of course the Bedouin also used to feed their horses high energy, high sugar content food such as dates. Prior to the 16th century in the UK, most goods were transported by pack ponies, not by wheeled vehicles. Wheeled vehicles were only used very locally, for carrying goods a couple of miles or so. Carriages only came into use at the end of the 16th century and they were very limited in use, just around London and the south east of England, mainly. The roads were so bad, but the pack ways were retained in good order. Fast trotting ponies could get even perishable goods such as fish to London from the north west of England in a very short space of time.
I guess that as far as military use goes, a lot would depend on your remounts. Remounts, I imagine, could be used to carry some of the high protein feed that was required whilst campaigning? Naturally grazing horses, as you say, require a long time at grass to capture the necessary protein and nutrients.
This is not accurate. In fact it is the opposite. Traditionally mounted warriors were limited in their engagements due to feed requirements. Most cavalries had to travel via terrain that had sufficient grass growth and water. This made them very predictable and also limited. The Parthians began the practice graining their horses as a main feed source which unlocked all of the other regions and terrains that had restricted them. Therefore, when Romans began their invasions of the Parthian regions, they would take routes that were thought restricting to cavalry ambush. The Parthians would carry high in starch and protein grain mixes that would supply their horses with much more feed than a typical forage style eating would. You have to also remember that horses take quite a longtime to eat when they are free range feeding. The grain allows them to quickly intake the starches and proteins that they require, in smaller doses as well. Rice, egg whites, bran, oats, barley, wheat, beat pulp, seed mixes and a few other mixes were made into feed balls that were very easy to carry.
This gives the cavalry free range now, to attack at will, from their desired choice of region and with sufficient time and resources. Free range and pasture limited cavalries suffer many other issues that are too lengthy to explain here.
The baggage trains for Parthian, Sassanian, Saramation and other such mobile cavalries in the Iranian tribes quickly figured out how not to be limited. Horses are much more a liability in warfare than people today can understand. As a horse person this is something that I feel must be addressed when people discuss horses in warfare today.