Running backs Reggie Bush of the Detroit Lions and Adrian Peterson of the Minnesota Vikings both were injured in the snow.
Bush suffered a calf injury while slipping during his warmup at Lincoln Financial Field in Philadelphia and was ruled out of his team's game against the Eagles.
Peterson hurt his ankle during the second quarter against the Ravens in Baltimore on a slippery surface that seemed more like an ice rink due to the swirling snow.
Because of the blizzard-like conditions in Philadelphia, leaf blowers were used during the first quarter when officials wanted to measure for a first down.
The Redskins, who play in the Washington suburb of Landover, Maryland, were experiencing their first snow game since FedEx Field opened in 1997 as they hosted the Kansas City Chiefs.
Heavy snow also affected the game in Pittsburgh between the Steelers and the Miami Dolphins.
The massive storm system dropped between 3 and 6 inches (7.6 and 25 cm) of snow on West Virginia early on Sunday before blanketing the Washington, D.C., metro area with its first accumulation of the season.