From the Wikipedia entry:

"After the completion of the Mercury and Gemini projects, NASA wanted a way to promote greater awareness among its employees and contractors of the impact they had on flight safety, the flight crews and their missions.[4] NASA wanted to use a symbol for spaceflight that would be well known and accepted by the public, similar to the recognition received by the United States Forest Service's Smokey Bear.

The idea for the Silver Snoopy award came from Al Chop, who was director of the public affairs office for the Manned Spacecraft Center (now called the Lyndon B. Johnson Space Center). He wanted to create an award featuring Snoopy as an astronaut to be given by astronauts in recognition of outstanding contributions by employees.[5]

Charles M. Schulz, who was an avid supporter of the U.S. space program, welcomed the idea of using Snoopy for the award. Schulz and United Feature Syndicate (the distributor of the Peanuts comic strip) agreed to let NASA use "Snoopy the Astronaut" at no cost.[4] Schulz himself drew the image the award pin was based on. He also drew promotional art for posters to promote the award program.[5] "