A coin drinking game. You'd have these huge fucking alcoholic dudes stumbling around to the table and flipping coins into glasses and the last person not to throw up or be unconscious wins the gold.
It would last for hours and hours and it would be fucking glorious.
Seriously though: skateboarding half-pipe, skateboarding freestyle and skateboarding game of SKATE.
Downhill Wingsuit racing
Real life rocket league
tug of war
Team Snow Shoveling race
Free for all King of the Hill on a humongus snow mound.
Snowball fight (teams of five, 10 minutes to build a fort around your flag, the first team to knock down the opponent flag with a well placed snowball wins)
Obstacle course (different courses every olympics)
Blowjob competition (Couples compete against each other, the woman performs a blowjob on the opposing male contestant and the first one to ejaculate loses)
A "biggest splash" competition that parralels 3 metre diving but the one who wins is the one who sends water the highest.
Waterboarding competition. How long can you be waterboarded before you die or give up? You are strapped to the table and as soon as you drop a pencil placed in your hand, you are released.
8-ball and Snooker
Strong man comeptition events
Gladiator fights to the death