Omaha has seen 12 Octobers with measurable snow since 1948 (13 now that it snowed in October of 2009!). Of those years, the subsequent winter went on to be in the warmest third 5 times, the near-normal third 6 times, and the cold third just once. Also, 6 of those 12 snowy Octobers were in El Niño winters, 4 were neutral, and 2 were La Niña. The top 3 heaviest snows in October (1997, 1991, and 1980) were all associated with warm winters to follow; 2 of the 3 were during El Niño events, and the third was a neutral year that leaned warm (it had a few 3-month SST anomalies at 0.5 but not for long enough to be defined as an El Niño episode). Omaha has never had a cold winter when there is an El Niño with October snowfall.
The story also follows for Lincoln and Norfolk. Each of these sites has had just one cold winter that followed a snowy October during an El Niño. Like Omaha, more of the snowy Octobers occurred in El Niño years than either neutral or La Niña years. Few of the subsequent winters were colder than normal, and many were warmer than normal.