A severe weather warning for rain and snow is in force for the western half of the Central Belt and Ayrshire until 8pm tonight.
Snow was hampering drivers on roads including the M74 around Beattock in Dumfries and Galloway.
The Met Office yellow - “be aware” - alert is for 20-30mm of persistent and heavy rain, with 2-5cm of snow above 200-300m.
A spokesman said: Please be aware of locally difficult travel conditions, either due to surface water flooding, given the saturated ground, or due to snow on some of the higher routes.
“The airmass is rather cold, with conditions marginal for snow.
“Any heavy precipitation will tend to swing the balance towards snow rather than rain, so there is the likelihood of some tricky conditions due to some settling snow, at least over some hilly areas.”
A separate warning for gales gusting to 70mph across the far north of Scotland is also in force until 8pm.
The Met Office said conditions would be worsened by more than 40mm of rain in places and hill snow across an area stretching from Lewis and Harris to Orkney and Shetland.
Snow could also accumulate at low levels in Shetland.
The spokesman said: “Please be aware of potential disruption to transport, with a number of factors contributing to the unpleasant, potentially hazardous, conditions.
Eight flood warnings were in force, including at Inverurie and Kintore in Aberdeenshire, which were badly affected by flooding last week, and around the River Don in Aberdeen.
Three of the warnings were for the River Isla in Perthshire, with the others for the Lyne Water at Romannobridge, near West Linton in the Borders, and from high tides at Golspie in Sutherland.
The railway line between Girvan and Stranraer has been closed until 31 January after damage was found to the Laggansarroch Viaduct, near Girvan, caused by Storm Frank.
Meanwhile, Nicola Sturgeon yesterday announced a £12 million fund for Scottish communities affected by severe weather.
The cash includes a £1,500 grant for every household, business premises or charity directly affected by flood water, and a £5 million fund for councils to replace damaged infrastructure.
The First Minister unveiled the funding boost as she visited the flood-hit north-east.
The area has been battered by heavy rain, causing severe disruption to travel, the evacuation of homes in some parts of Aberdeenshire and two severe flood warnings for Inverurie and Kintore.
It follows flooding across other parts of the country, including Tayside and the Borders, as a result of Storm Frank.
The funding is in addition to the £4 million announced by the Deputy First Minister in his budget statement, bringing the total package of support for those affected by the adverse weather to more than £16 million.
Ms Sturgeon has been under pressure from opposition parties to spell out what extra funding will be allocated to flood relief.
An extra £5.8 million will be made available to support households and business properties.
Councils which have suffered the most damage as a result of the flooding have been allocated a share of the fund, but people in any part of Scotland who have suffered flood damage can apply for a grant.
In addition to flood relief support, businesses whose ability to trade has been severely affected by flooding will be able to apply for an extra grant of £3,000 funded by the Scottish Government and administered by their local authority.
Additional funding of up to £5 million will be made available to councils to replace infrastructure severely damaged by flood waters, including support for the reinstatement of the A93 between Ballater and Braemar.
An Agricultural Floodbank Restoration Grant Scheme of up to £1 million will also be made available to farmers to restore damaged floodbanks, and discussions will continue next week with the industry on how the Government can support them through severe weather.
Ms Sturgeon said: “In the face of devastation Scotland’s communities have rallied together and shown real strength. I have met with some local business owners who have made a real difference by offering vital support and once again I am amazed by the determination and dedication of all of our emergency services who are working around the clock to save homes and livelihoods.
“We do not yet have confirmation of consequentials coming from UK Government flood funds - however, now that the picture of those who need support is clearer, the Scottish Government is acting now to make sure that the people who need help get it.”