Vehicles were stranded overnight and a stretch of the motorway remains closed this afternoon, between junction 24 and junction 21, westbound, and junctions 20 to 22 eastbound, 'due to strong winds' and as efforts continue to clear the road of stranded HGVs.
The A66 and A628 remain closed, Highways England said.
Highways England have set up a diversion around the problem area.
Transport Secretary Chris Grayling says the severity of the weather conditions that led to the partial closure of the M62 means it is "difficult" to take steps to stop it happening again.
Mr Grayling was asked about the closure of the motorway during a visit to Leeds today, where he was speaking at a transport conference.
He said: "It has been a really difficult couple of days across the Pennines, where people have been stranded on the motorway, not just in this area, it has been around the country.
"Of course the Pennines are used to snow, but this level of winter experience happens very rarely. We haven't had red warnings in this country for a long time.
"And so it is difficult to take steps to prevent it happening when these unusual events do happen, but I know on both sides of the Pennines we have got Highways England, we have got people from the police, local authorities, in some cases the Armed Forces, and on the railways, rail staff trying to get things back to normal."