There are a number of factors that influence how a lake freezes after the water gets cool enough to set up. As Matt pointed out moving water is much more difficult to freeze which is why lakes take a long time to set up when it's really windy and why ice where there are currents, like in flows and out flows or springs, is so dangerous. Areas with heavy vegetation or even fish activity can affect the ice production.
The depth of the water has a dramatic effect as well. For example locally one lake we ride has an average depth of 20' and we are riding on it usually by early December. Another lake approximately the same size with an average depth of 75' doesn't usually freeze until the end of January.
After a skim ice has set in, the air temp really comes into play. If it's well into the single digits or lower and there is no wind and little current ice grows amazingly fast. However, if it gets a layer of snow on top up it, the insulating effect of that snow will stop ice production. Worse yet, as the water below the ice is above freezing, the ice will actually start to degrade from below if the insulating layer isn't removed. (see pic from one of our ice inspections) There is a common misconception that snow makes ice, in fact it does the opposite.
This is why we always hope it doesn't snow until we get a good base layer of ice. Snow kills ice if the ice isn't substantial before the snow comes.
In the later part of the season snow is a benefit as it insulates the ice from the warmer air temps and the solar gain. Once that sun comes up and gets on the ice at a high angle things change quickly. Add wind to the mix, flexing a weakened ice sheet, and the ice can blow out in a day.
We had ice here in northern New England, then got hit with too much snow which weighted the ice sheet and caused water to come up over the edges and through cracks making a crappy slush situation. Once you have that you are boned as the slush under the snow never freezes, is warmer than the ice and you effectively have the ice being melted from above and below. The only solution is a warm up which we got. And a ton of rain. Two days later we dropped into single digits and went from nearly losing rideable ice to some really pristine ice.
Bob Dill has an put together an excellent resource on ice dynamics. We recommend it to our students and anyone who rides ice on a regular basis .
Ice is a surprisingly dynamic thing.