The Soviets were pretty keen on live fire tests - their very first test of a staged thermonuclear device was air dropped. Air drop tests were fairly common, AFAIK the only people who have done a live launch of a nuke on a missile were the Chinese.
The Soviets tested an R-13 SLBM with a live warhead in 1961. A Polaris SLBM with a live warhead was tested by the US in 1962 as part of Operation Dominic. I don't think either country did a live test of an ICBM though.
The US tested a live Polaris in 1962. They were responsible enough to cook it off at 11,000 ft, a real combat launch would likely have been detonated closer to the ground.
