In the 1920s there was an overblanket that was fastened on to cribs and strollers and it was called a security blanket because it was meant to keep the babies in. By World War II it was being used in a more figurative sense and Charles Schulz, with his Peanuts cartoon, brought it into a fully figurative use. ( source )

The origin of wet blanket is very literal. Way back in the day (the 1600's day) it was recommended that people keep a small wet blanket near their fires in case they got out of control. Then they would have a quick way to put the fire out before it got too big or out of control. ( source ) Throughout the many years the phrase morphed from literal to figurative and it showed up in 1871 as the way we use it today - someone who spoils other people's fun by failing to join in with or by disapproving of their activities.