This is really a bad idea - not impossible, but not likely to be much fun, either.
I have 100,000 miles touring experience - most of it in the U.S. and Canadian Wests.
Back in 1990, I got stuck in the Cascades by a snowstorm in early June.
By your user name, I am guessing that you might be from Portugal, Spain, or Italy.
If so, you probably don't have much winter touring experience.
And it's not just the passes. You will face tough conditions all the way through the Rockies.
It is hard to predict any one year, but this is an El Nino year in the West.
Already, the snow levels in most Western mountains are higher than average.
(Less so in the Northwest, more so in the southwest)
Here is a link to snow levels which is updated regularly:
http://www.wrcc.dri.edu/snotelanom/basinswe.htmlMay snowstorms in the North Cascades and Northern Rockies are common.
You can wait them out in the valleys - where it might be 5C, rainy, and windy.
Most campgrounds and other National Forest / National Park facilities do not open until late May.
McKenzie Pass in Oregon may or may not be open that early - you can always use Santiam Pass.
But what that means is that you will be cycling in cold, wet, windy weather.
Craig Pass in Yellowstone does not open until May 21 - few services until June.
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If you plan on leaving in late April, I would STRONGLY urge you to go east-to-west.
Even then, you will experience some cool, wet weather in the eastern mountains.
But it won't be anything like May in the West.
Cycling the West in late June will be far, far more enjoyable.
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Late May in the Sierras of California in an average snow year in nice weather:
(The reason I don't have many pix of heavy snow in the spring is because I avoid touring in those conditions.)