Most of the water within the Arctic circle is frozen because of how cold the weather is in that regain of the world. The regain does have some non-frozen water like the Mackenzie river. 

The Mackenzie River is one of the largest rivers in Candida. 

The Mackenzie River (great river) is the largest and longest river system in Canada and the second largest on North America second just to the Mississippi River  in North America. It flows through a long isolated region of forest and tundra entirely in the country's Northwest Territories although its many tributaries reach into four other Canadian provinces and territories. The river's mainstream runs 1,738 kilometers (1,080 mi) in a northerly direction to the Arctic Ocean, Draining a vast amount of water. It is the largest river flowing into the Arctic from North America,

Rivers normally begin in mountains or large hills where they form from streams called gullies from a lot of collected rain water and or melted snow. These gullies will either grow larger after collecting more water or they will meet with streams and add on to that water. When streams converge (meet) the smaller of the streams is known as a tributary. The point at which the two streams meet is called a confluence. In order to form a river it takes many tributary streams.The Mackenzie River has many tributaries to name a few Great Bear River,Great Slave Lake and the  Keele River.

The Delta of the Mackenzie River is a large amount of water. Not all rivers flow north to south like many people believe. 

The delta is a maze of channels, cutoff lakes and circular ponds  bordered by the Richardson Mountains in the west and the Caribou Hills in the east.

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The Mackenzie River has many small tributaries, this picture shows some of them

I think that the Mackenzie River started because of melting show or ice that started to flow downhill. Then the river has small tributaries that made the river flow stronger and stronger until it reaches its delta in Candida.  "Significant evidence exists that roughly 13,000 years ago, the channel of the Mackenzie was scoured by one or more massive glacial lake outburst floods unleashed from Lake Agassiz, formed by melting ice west of the present-day Great Lakes. At its peak, Agassiz had a greater volume than all present-day freshwater lakes combined. This is believed to have disrupted currents in the Arctic Ocean"

1. Natural Resources Canada. 2007-12-20. Retrieved 2008-06-16.