How standard was the naming of horses in Europe from the Roman times up until the early modern era? I know that's a big time span but I'm sure someone knows. Was it universal practice for lords, knights, or wealthy men-at-arms to give a name to a warhorse (or any other type of horse, including pack horses) during the early Middle Ages or onward? Was this practice continued with lancers, Hussars, cuirassiers, or arquebusiers of the 1600s?

Anecdotal evidence gives that at least emperors most prized horses where indeed given names. And sometimes even appointed to be consuls (unconfirmed myth, but funny anyway) :D

Wiki has a list of historical horses, maybe you can find some more leads there

http://en.wikipedia.org/wiki/List_of_historical_horses

I would guess that since trained horses represented significant to immense value, they would be veery well taken care of, and out of the respect and seriousness of maintaining a major investment, also given a name.

This is also a guess, but horses were trained, and in that era were often employed in groups such that individual distinction would have had some advantages. Just about any present day animal trainer uses names in this kind of situation. My daughter's first ride was on a rodeo and penning trained horse was named "Doc" as in short for doctor. "Doc" could do just about anything in response to voice commands, whistles, and several hand gestures from quite a distance away from its owner. Although, I am not sure how good his arithmetic was. (He could count out several low digit numbers such as 1 to 4 by tapping the ground with a hoof. I don't think addition, subtraction, or multiplication were ever attempted though.)