Just as a running river does not freeze, waterfalls (unless subjected to sudden extreme and unnaturally low temperatures) don't either.

Here in New England, there are many places where the space for homes and highways have been literally hewn from stone. During the warmer months, rainwater runs down the side of these man-made cliffs with little fanfare. During the colder months, however, the trickling waters freeze just like icicles on the edge of a roof. Rather than hanging down off of an overhanging ledge on a house, however, the icicles follow the contours of the cliff making what looks like a frozen waterfall. Personally, they are one of my favorite winter phenomena.

It may look like a rushing waterfall, full of kinetic energy, has been suddenly stilled, but in reality these waterfalls of ice were formed relatively slowly, by slow moving-water.