The following map shows the median (middle date) of the "first measurable Snowfall" each Autumn in the Midwest as well as the Plains states. The map was produced by the Midwest Regional Climate Center and is based upon the 1981-2010 data period. This time period corresponds to the current 30 year climate normals. The 30-year climate normals are re-calculated every 10 years. The next 30-year normals will not be calculated until the year 2012.
Information about the Lincoln, NE, snowfall climatology can be found underneath the map.
Lincoln's Snowfall Statistics: http://snr.unl.edu/lincolnweather/data/snowfall-statistics.asp
Lincoln's Snowfall Climatology: http://snr.unl.edu/LincolnWeather/data/snowfall.asp