We know vaccines painful, and by comparing horses at rest with horses getting vaccinated, we've been able to determine how they express pain visually. By looking at horses with disorders like colic, broken bones, wounds, and so on, we can determine their facial expressions during more severe pain.

At zookeeper school we were drilled through the pain faces of the most common lab animals and livestock. Nowadays I believe this has become a routine lesson in all animal related fields, but the general public still doesn't know that this is a thing that exists.

Here are all the pain face/grimace scales I've been able to find. Please study them if you interact with any of these animals on a regular basis: