In the US, men 18-25 have register for Selective Services, and in other countries there is mandatory military service. Are wizards exempt from registering for the draft/doing mandatory service?
Wizards are known to fight in Muggle wars...
From the Pottermore History of Magic in North America: The 1920s
The wizards of America had played their part in the Great War of 1914-1918, even if the overwhelming majority of their No-Maj compatriots were ignorant of their contribution. As there were magical factions on both sides, their efforts were not decisive, but they won many victories in preventing additional loss of life, and in defeating their magical enemies.
Considering there was a draft for the Great War (aka World War I) and wizards did fight, we make the conclusion that some were drafted.