Yes, medieval horses were smaller. Remember that many modern horses, especially racehorses, have been bred for their size for several hundred more years than a medieval horse. There's not really much to say here.

Most of what we know about medieval horses comes from archaeology - basically just digging up the skeletons of medieval horses - and the archaeology is very clear. A major study on medieval horses given the snappy title of In Search of the 'Great Horse': A Zooarchaeological Assessment of Horses from England (AD 300-1650) was completed last year and that offers a significant body of evidence. From 1066-1350, they found nearly 400 partial or complete skeletons. The average height of these horses was 1.35m, though there was typically some variation between 1.25-1.4m in height, with a couple of outliers at 1.6m.

For an idea of what that looks like, this gave them similar proportions to the Mongolian wild horse or Dzungarian horse, which have the same average height. If you were a medieval nobleman and bought an average horse, it would have been about 1.3m tall. To put that into perspective compared to other modern horses and horses across the entire Middle Ages and Renaissance, the study helpfully includes this chart condensing all that lovely data into one box plot diagram.

Height was not considered all that important to medieval noblemen, they cared more about durability and reliability. There was no point to a fast horse if one arrow was going to make it reel in pain and panic. Size was not that desirable for two reasons. Firstly, it made the horse a bigger target for enemy archers. Secondly, it made the horse harder to mount and dismount. When English knights were fighting in Wales in the 12th century, contemporary writers such as John of Salisbury and Gerald of Wales noted that the knights had a lot of trouble mounting and dismounting at speed because their tall saddles made their position too high to simply jump on and off; they had to use their stirrups as a step. This slowed them down enough that their preparations for battle were sluggish and gave their more lightly armed Welsh adversaries an advantage in battle as knights thrown from their horses struggled to get back onto them. They seemed to learn their lesson though, because the practise of rapidly leaping on and off of horses is a common theme of medieval accounts of battles. Height was not a desirable trait to medieval knights, because what they wanted was a horse that could take blows, that they could mount and dismount as fast as possible, and could sustain their energy for hours at a time.