No, moving water can never freeze completely.

The Niagara River handles 212,000 cubic feet of water per second. The average depth is approximately 16 feet with a flow rate of 4 to 8 miles per hour. The Niagara River does not freeze over. The Falls of Niagara and the river below the Falls does not freeze either. The volume of water going over the Falls, the depth and speed of the water below the Falls also precludes freezing. The water will not be stopped or frozen solid. The ice bridge however does form at the base of Falls and over portions of the Niagara River below the Falls. The ice bridge is formed in late December to the end of February and into mid March dependant on the weather. Lake Erie which drains into the Niagara River is a large lake but rather shallow. By the end of December, the entire lake surface is frozen over. Although an ice boom has been put into place since the 1960's at the mouth of the Niagara River and Lake Erie. The boom holds back most of the ice but not all. When the ice goes over the Falls in volume the ice freezes to the edges of the gorge and builds upon itself until the river is covered in this giant layer of ice. This layer has grown to eighty feet thick in the past and currently 40 feet is not uncommon. The Falls of Niagara still flows as does the water under the ice and the ice shelf seems to rise on layer of air that builds under the ice surface. The American Falls have frozen over on six occasions since the keeping of records began. Each were attributed to ice jams that have actually curtailed the flow of the American Falls to mere trickles. Unlike the Horseshoe Falls (which has never frozen over), the American Falls are susceptible to freezing because of the small amount of water flow. Normally the American Falls has a peak mean flow of 10,000 cubic feet of water per second. The winter mean water flow is reduced to less than 8,000 cubic feet of water per second. This minimal flow is barely sufficient to cover the rock face of the Falls. During harsh winters, ice frequently built up at eastern end of Goat Island causing an ice dam to reduce the water flow to the northern channel which feeds water to the American Falls. As a result water flow is restricted sufficiently that any remaining waters quickly freeze over.

Yes actually i remember learning in school that it did actually completely freeze over once...way back when...like in the 30's or something...

No, not completely. But in the Arctic, the Mackenzie River freezes solid enough to become an icy highway every winter.

"The number one question everyone asks about this set of images is, "Does Niagara Falls ever really freeze over like this?" And the answer is yes. During an extended winter cold snap a hardened crust of ice can accumulate over parts of the falls -- American Falls in particular -- creating an amazing, naturally-formed ice sculpture, if you will, that has been known to reach a thickness of 50 feet. Neither the river nor the falls ever freezes solid, mind you. The water continues to flow beneath the ice at all times, albeit reduced to a mere trickle on rare occasions when ice jams block the river above the falls." Taken from: http://urbanlegends.about.com/library/bl_niagara_falls_frozen2.htm Follow the link for the rest of the story and some really neat pictures.

An ice jam in the upper niagara river once reduced the flow of water over the falls to "a mear trickle" back around 1912 or 13. The "Jam" only lasted for a few hours.

Yes, it has like in the 1920's..