The yellow warning of snow and ice for Fife has now been extended to Friday.
The area is already under a Met Office warning for ice and snow, with showers throughout today and becoming heavy at times.
Transport Scotland has warned drivers that road conditions are likely to become difficult, with the possibility of bridge restrictions.
The snow is now set to continue until Friday, though by then it could turn to sleet and rain over coastal areas.
The Met Office said of the situation: “Heavy snow showers will continue through Thursday and Friday, although perhaps more of sleet and hail near some coasts.
“Over exposed high ground, snow will drift in the strong winds. Travel delays on roads are likely, as are public transport cancellations.
“There is a chance of power cuts, while services such as mobile phone coverage may be affected.
“A few rural communities may become cut off.
“In addition some roads and pavements will turn icy, increasing the chances of accidents or injuries.”
Meanwhile, as the snow continues on Thursday, a warning has now been issued for strong winds.
The Met Office said pof Thursday: “Very strong winds will affect parts of the UK during Wednesday night and into Thursday.
“The strongest winds are expected to transfer eastwards across the warning area before clearing by early afternoon.
“Road, rail and ferry services may be affected, with longer journey times and cancellations.
“There is also a possibility that some bridges may close. Power cuts may occur, with the potential to affect other services, such as mobile phone coverage.
“Injuries and danger to life from flying debris are possible, along with some damage to buildings.
“In addition, large waves are expected to affect some western coasts with beach material being thrown onto sea fronts, coastal roads and properties.”
A spokesman for Transport Scotland said: “Our gritting teams and patrols will be out across the trunk road network during this time. There is plenty of salt available for treating the roads and the winter control rooms are constantly monitoring conditions to make sure our public information is up to date. Ministers have also been briefed on the situation.
“The weather is likely to cause some difficult conditions on the roads, so we would ask motorists to plan their journeys in advance and drive to the conditions.
“The high winds may also lead to bridge restrictions, so drivers should check Traffic Scotland before they set off to make sure that their route is available, either through the new mobile website or the @trafficscotland twitter page.
“For people planning to travel by rail, ferry or plane, it’s a similar message – you should check with the operator ahead of time to find out if your service has been affected by the conditions.”
ScotRail plans to run a full service over the coming days.