We have some previous answers about people building snowmen specifically, but they probably apply to playing in the snow in general:

Where/when did the tradition of building snow men originate? (by various users including some deleted ones)

From Wikipedia: "The Miracle of 1511 (Dutch: De sneeuwpoppen van 1511) was a protest in Brussels, Belgium, against the country's government, in which the locals protested by building approximately 110 satirical and pornographic snowmen." Can I please get more info and the overall context of this? by sunagainstgold

In the film "Django Unchained" Django uses a snowman for target practice. Are snowmen actually things people would make during the 1850s or was it just used in the film as an artistic liberty? by u/lord_mayor_of_reddit