[Blue Jays]

"....Do they have bike races in the snow and ice?..."

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Yes.
Here is Andy Hampsten on his way to Giro d' Italia victory at the Gavia Pass:

[gura]

Bob Roll stated in Bobke II that on the way down the Gavia he got off his bike and ran uphill trying to warm up. He blacked out from hypothermia after crossing the finishing line.

[Blue Jays]

Great interview with Andy Hampsten on his classic Giro d' Italia race victory and the epic struggle of that historic day.