Both nations had experience in high-altitude flying. U.S. and Soviet engineers adapted high-altitude flight suits to their spacecraft life support systems to ensure survival in the event of an emergency.
Yuri Gagarin wore a spacesuit similar to this one. It had a pressure layer that formed a sealed environment and allowed him to breath. Beneath that layer he wore thermal clothes. Gagarin needed this suit to survive the high-altitude parachute drop that concluded his flight.
Alan Shepard wore a modified version of a U.S. Navy Mark IV flight suit for his Freedom 7 mission. The silver-colored coating was meant to increase his visibility if an emergency rescue was needed.