I declared war on the nation of cEviN keY this morning. However, I apparently have the option to launch a nuclear weapon against him, despite being at war for less than four hours. Instead of the normal (paraphrased) "Your nuclear weapons are being readied for launch" text, I just have the normal launch button.
If I had to guess, it might be an error caused by fighting a war against the exact same nation a few weeks ago. Note that I have not actually tried launching a nuclear weapon to see what would happen.
Edit: I did try launching one (for science!), and got the red exclamation point error message, informing me that I had to wait 24 hours. So it seems like the glitch was only on the precursor screen, and didn't actually carry over into a valid launch.