Witnesses spoke of up to 6in of snow falling, causing chaos for cars driving on Telegraph Hill and leaving emergency services struggling to reach the scene.
Devon and Cornwall Police and firefighters from Devon and Somerset Fire Brigade said they were dealing with the incident.
Sue Rolfe, 56, was forced to leave her car on Telegraph Hill and walk to The Exeter Court hotel where she works after police closed off the road.
The receptionist said: "They have tried to open the A38 with snowploughs but that hasn't worked. Everyone is stuck. It's chaos. It's still snowing very hard. It's come down so quickly."
She added that the hotel was nearly full, and staying open all night to help drivers leaving their cars.
Police said the road was closed shortly after 9pm yesterday due to "significant heavy snow" and that up to 200 vehicles were stuck at the location.
A force spokesman said: "We have a reference centre open and we've got multiple localities for the rest of the force, Devon and Cornwall, with vehicles stuck."
Meanwhile, weather forecasters last night warned people across the north of Scotland to brace themselves for two more days of wintry conditions.
Almost 300 schools were closed yesterday as the heaviest snowfalls of the winter brought chaos to road, rail and air travel.
Forecasters last night warned further snowfalls and freezing temperatures were expected across the Highlands, Aberdeenshire, Orkney and Shetland today and tomorrow.
Councils across England say they are running out of road salt, and the AA warned the shortages had created a "road safety crisis".
As blizzards swept across Grampian yesterday, police urged motorists not to travel unless absolutely necessary.
Snow closed some major roads in the area, while others were blocked by jackknifed lorries or overturned cars.
At one time yesterday, up to 30 motorists were feared trapped in their vehicles near Colpy on the A96, the main road between Aberdeen and Inverness.
In Aberdeenshire, 145 of the council's 174 primary, secondary and special schools were either completely or partially closed in another day of Arctic conditions. In Moray, a total of 39 secondaries and primaries were shut, while 63 schools were closed or partially closed in Highland, and 26 were closed in Aberdeen.
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Written by Frank Urquhart