Michael Laudrup's side take a 2-0 lead into the game after claiming victory in the opening match at Stamford Bridge.
"Tonight's Capital One Cup semi-final second leg tie with Chelsea at the Liberty Stadium (7.45pm kick off) is on," read a statement on the club's official website.
"Despite the snow, the Liberty pitch is in good condition with referee Chris Foy happy with the surface following an inspection.
"The surrounding areas outside the stadium have been classed as safe but we do ask supporters to be cautious when travelling to the stadium and entering the Liberty due to the current weather conditions.
"Some bus services have been cancelled, so we advise fans to check with their local travel operator."