Note that Accuweather weighs in on the cool April and May for 2013, actually reducing tornadoes so far. The link is here. When I was a boy, we typically hit 80 degrees in Arlington in early May, and 90 by late May, but often had strong cold fronts that would drop the highs for following days to 60. Heavy spring thunderstorms were frequent in the 1950s, but less destructive, because the tree canopy was not as high and there wasn't as much development.
Update: May 20, 2013
This has been a terrible period for the southern plains, especially around Granbury, TX (where I almost got an IT contract with Texas Energy in 1988), and today south of Oklahoma City, in Moore, which I have driven through on I35 many times. The area where I35 runs was hit by an F5 in 1999, with 300 mph winds, the strong surface winds ever measured on Earth. (On Neptune, they are 900 mph.)