The Met Office is predicting the temperature will barely rise above 2c or 3c for the rest of the week with freezing temperatures overnight.
Weymouth, Dorchester and most of South Dorset could have bright and clear spells tomorrow and escape further snow until Wednesday.
Widespread hard frosts should continue with wind speeds rising to 21mph as the snow threatens again later this week.
The cold conditions are expected to continue this week for the rest of the country too with the risk of icy surfaces and further snowfall more likely in the east.
The south west may turn a little less cold next week but could be more unsettled as rain, sleet and snow tries to push up from the south.
The Met Office is adopting a cautious approach and has not yet made any predictions for the rest of the winter.
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