You may still on occasion encounter this term for a knight's warhorse, though these days it’s almost always employed by writers of historical novels.
A recent work which is a science-fictional variation on the theme is Timeline by Michael Crichton (1999). The hero is sent back by time machine to medieval France but misses the last bus home. As a result he finds himself stranded in the middle of a civil war, having to cope with the armour and equipment of the well-dressed knight:
This horse was gigantic, and covered in more metal than he was. There was a decorated plate over the head, and more plates on the chest and sides. Even in armor, the animal was jumpy and high-spirited, snorting and jerking at the reins the page held. This was a true warhorse, a destrier, and it was far more spirited than any horse he had ever ridden before.
The presence of the page is actually the clue to the name, since the person who led the horse, often the knight’s squire, always walked on the left side of the horse’s head and so held the horse with his right hand (Latin dexter, on the right).
Off-duty, knights preferred a less spirited and more comfortable mount. This was the palfrey, a short-legged, long-bodied horse which proceeded at a gentle amble. A palfrey was also often ridden by women. Its name comes from Latin paraveredus, a bilingual concoction of Greek para, besides or extra, plus the Latin veredus, a light horse.