The icy conditions are expected again overnight and Monday will be a chilly one again with most areas feeling like -2 in the bitterly cold winds.
There could even be snow on the tops of hills as the showers are forecast to sweep over the county are expected to turn wintry in places.
Things are expected to warm up slightly over the course of the week before temperatures fall again in time for next weekend.
The Met Office forecast for Yorkshire in full:
A few early showers in the west, otherwise cold, dry and sunny. A strong, chilly wind will develop, eventually dragging heavy showers off the North Sea into eastern areas during the afternoon, but remaining dry with sunny spells further west. Maximum temperature 7C.
Showers may continue in the far east overnight, but for many areas it will be dry, clear and frosty. Gusty winds will ease inland, whilst remaining windy along the coast. Minimum temperature -2C.
Another dry, cold and frosty morning with light winds and plenty of sunshine. Cloud will thicken during the day with some rain and perhaps hill snow arriving during the afternoon. Maximum temperature 8C.
Outlook for Tuesday to Thursday:
Likely cloudy on Tuesday and Wednesday with occasional mainly light rain and light winds, and generally feeling milder. Hill fog likely. Sunny spells by Thursday, with wind and rain overnight.