For a large part of the year some of the best roads in cycling do not exist. Snow shuts them in autumn, and in spring a plough crew works uphill for weeks through walls of snow taller than the machines, until one day the barrier goes up.
Nobody can tell you in advance when that will be. It depends on how much fell, how deep it packed into the cuttings, and whether the avalanche paths above the road have run yet. Every road here has opened in April at some point in its history, and every one of them has stayed shut into July.
So do not plan around a date you read anywhere, including here. Learn the shape of the year instead: that the Beartooth is usually the last way into Yellowstone rather than the first, and that a Stelvio trip in early May is a gamble where early September is not.