UPDATED 1.14pm: Snow has been falling in Canterbury from south of Ashburton, inland to the Alps.

Speed limits are down to 60 km/h in many places, and police say chains are essential on most routes.

People in Canterbury can expect brief relief from the cold snap by around midday.

Further falls are expected, but a finer weather pattern is emerging in the short term with snow retreating to the north of the region as the morning goes on.

Metservice reports there will be some sleety showers late this afternoon and these will reach the plains and central Christchurch.

Snow flurries are possible though in Southland and Otago over the next 24 hours.

Lewis Pass, Rahu Saddle and State Highway 73 were closed overnight and this morning.

They've now reopened but motorists are being advised to carry chains.

All southern State Highways are now open except State Highway 94 Milford Sound to Te Anau and there are still some restrictions in place.