Icecrown River is a freezing, often frozen river cut across Icecrown Glacier from the upper corner to Lake Wintergrasp below, northwest to southeast. The river cuts down through Icecrown Glacier, much of it is frozen over as well, at least on the surface. It's too wide to leap across and too fast and cold to swim. Plus the banks drop sharply to the water, all along its length. They were too high, steep and slick, for anyone caught in the water to climb back out. It had no official name so Brann Bronzebeard named it Icecrown River.
Icecrown River in World of Warcraft
Since the former Lake Wintergrasp appears to have been almost completely emptied, it is likely that this river no longer exists. Furthermore, there are no rivers in Icecrown, which makes it even more possible that the river no longer exists.