I've been in IT for around 20 years now, and look to still be working over the next 10 or so. The company I'm with currently still has benefits like education and pensions, things that have disappeared from the environment to a large extent.
They happen any season, though the highest frequency is during the summer months they have been known to happen even in wintertime, and in those cases are even more dangerous (trying to find a grayish-white funnel with grayish-white clouds and white snow covered ground while snowing is extremely difficult). Basically any combining of cold dry air with warm humid air has a potential for creating tornados and funnel-clouds. In winter, such combinations are often what bring on your basic snow storms.
In the south, winter is the most dangerous time when it comes to tornadoes. For example, just from February, 2008, there were 12 killer tornadoes with 59 fatalities. Snow had nothing to do with it, there were your average supercell thunderstorms combined with warm, humid air from the Gulf mixing to create a dangerous situation.
On a clear disk you can seek forever.