Sgt Steve Pick told BBC Newcastle: "What we're suggesting is that people don't travel. If you need to travel, take the necessary precautions.
"Make sure you have a mobile phone, leave plenty of time for the journey and take a great deal of care."
But he said most of the roads were quiet because motorists had heeded the advice at stay at home.
In the Durham and Teesside areas, main roads have been gritted and are passable with care, though many minor routes remain problematic.
Anyone who does travel is urged to plan their journey and be prepared for disruption.
The Highways Agency said drivers should also carry a blanket, warm clothes, food, a hot drink and a shovel.
More snow is forecast for north-east England on Saturday and Sunday, while overnight temperatures from Friday through to Saturday are expected to fall below freezing.
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