Police are urging drivers to only take to the roads if necessary and to expect delays if they do.
Sergeant Andy Barron, from the Western Area Roads Policing Team, said anyone getting in their cars should make sure they have warm clothing with them, a spade and a fully charged mobile phone.
He said most of the main routes are open, although the M62 is down to one lane.
He added people seemed to have heeded early warnings from weather forecasters as there seemed to be less people on the roads.
There have been three accidents reported in Calderdale this morning.
At 6.20am, a BMW 5 hit a parked Mercedes on The Hough in Northowram. A woman suffered minor injuries.
At 7.01am, a Peugeot 206 hit a lamp post on Royd Terrace at its junction with Skircoat Moore Road in Halifax. One person suffered minor head injuires and cuts.
There have also been reports of buses getting stuck, including in Norton Tower and Bell Hall in Halifax.
The police have also issued the following advice for driving in the snow:
Make sure all your car lights are working and you have no failed bulbs. Ensure that dirt, salt and snow is cleared away from light fixtures.
Always ensure all windows are fully cleared of snow, frost and condensation before setting off on a journey - it is illegal to drive with obscured vision.
Also clear snow from the top of the car as this can fall down and obscure your windscreen while you are driving.
Keep windscreen washer fluid topped up as windscreens quickly become dirty from traffic spray and salt from the roads.
Make sure you have sufficient fuel for your journey. Keep the fuel tank topped up.
Give yourself extra time for your journey and drive at a constant speed. Accept your journey will take longer and don’t take risks.
If you get stuck in the snow stay with your car. In an emergency, if you do need to leave it, park it out of a main traffic route, where it won’t cause an obstruction when conditions ease. Leave a contact number on the inside of the windscreen and return to your car at the first opportunity you have.