2001 Impala intermittent start

My 2001 Impala starter dosesn't like to work in cold weather. When I hold the key in "start" position, nothing happens. When I let it up, in "run" position, the starter spins briefly until the motor fires. If I do that a couple times, the engine is running. Is it a bad ignition switch? I've changed the starter, with no change in symptoms. Also note, the "security" warning comes on sometimes after I've started the car this way. The starting problem only happens when it is cold - I believe only when it is cold inside the car. If the car sits in the sun, and the interior is warm, I haven't noticed a failure. Everything works great when it's above about 40 degrees F outside. :)

On a possibly related note, last summer my signal light flasher didn't appear to work intermittently - usually only on hot days. I could get it to start working every time by briefly activating the 4-way (emergencey) flashers.