"icy river" is correct and usable in written English.
You can use it when describing a body of water that is especially cold. For example, "The icy river was so cold that I couldn't bring myself to take a dip in it."
He went down to the hole he kept open in the icy river, crossing himself as he walked past Mink.
A man stands on a bridge, staring into the icy river rushing below him and contemplating his life.
Near the valley floor, we veered onto a rocky trail that tracked an icy river called the Chandra.
An icy river crossing numbs our feet, but does, as Grace points out, at least clean off the mud.
There's this feeling, I think, akin to dunking yourself in an icy river in January, voluntarily: hold your breath, try not to panic, try to enjoy yourself.
In the distance, an ornate Buddhist temple glinted next to an icy river, and further beyond, a burgundy and silver gilded palace clung to the mountainside.
Footpaths worn into loose rock on mountainsides can be as narrow as the width of two hiking boots, with thousand-foot drop-offs that can send any stumbling climber into an uncontrollable slide to icy glacial rivers.
Monday was Russian Orthodox Epiphany, and roughly 30,000 Muscovites lined up to dunk themselves in icy rivers and ponds, city officials said.
In the spawning season, icy rivers turn into roiling torrents of red fish as tens of millions of Pacific salmon make their way inland to spawn.
It was tough going – huge peaks, glaciers, snowfields, icy rivers … One day we reached a high-altitude plain filled with boulders covered in petroglyphs.
Most but not all of these wild salmon are caught in the long and icy rivers of Alaska (the Skeena comes from British Columbia and the Willapa from Washington).
