H. E. Taylor wrote:

When does the tornado season in the States usually begin?

I don't believe there is one per se -but a recent report said the
season has started early.

Whilst we are on the subject, anyone care to explain the legend on this
site:
http://www.spc.noaa.gov/products/wwa/ ?

And whilst I am draining the burden of all crania, may I ask if there
is any corresponence with extreme cold weather anywhere on an arc of 90
degrees of their occurence while there are extremely high temperatures
some 15 degrees down the road? (Wouldn't that be an handy tool if it
were so?)

Nah!

Not possible.