Snowballs show up in many pictures throughout the late mediaeval and early Renaissance; they appear in the Census at Bethlehem as painted by Pieter Brueghel the Elder in 1566, as well as in the version by his son, Pieter Brueghel the Younger, done in 1610. This version is notable as it shows snowballs not just being thrown but being force-fed to a woman by a small crowd. Such a practise likely originates from an apocryphal story about St. Francis of Paula from the early fifteenth century, in which he, upon an encounter with Satan, makes seven snowballs, which he threatens to eat if Satan does not leave him alone.

The first recorded image we have of a snowball fight, however, is a 1390s-1400s fresco in the Castello del Buonconsiglio.

For more information about the history of winter divertimenti, I highly recommend The History of the Snowman by Bob Eckstein, from which I have learned everything I know about snowballs.