Well, yes, up to a point.
Although the last time troops charged with bayonets was during the Korean War in 1951, bayonets are still used by the marines:
And horses? A few charged into Afghanistan in 2001 during the initial attacks, but the warriors riding the steeds brandished not bayonets, but laser pointers to direct air strikes. The army’s last cavalry charge was against the Japanese in the Philippines in 1942. As World War II was ending, the few remaining horses that had been used for transport and supply duty were supplanted by trucks and jeeps.
Today we still see them prancing on ceremonial occasions.
Hat tip: video via Slate