An emergency funding scheme has been opened for local authorities in the wake of the severe weather.
The Scottish government said it would consider applications for financial assistance through the Bellwin Scheme, after Scottish Borders Council requested help.
The discretionary fund is designed to help councils which face extra costs as a result of large-scale emergencies.
The move comes after major disruption caused by the "Beast from the East".
Yellow warnings for snow and wind remain in place until Monday.
The Bellwin scheme was last activated after Storm Frank caused severe flooding at the end of 2015, with millions of pounds given to repair damage in the Borders and Aberdeenshire.
Finance Secretary Derek Mackay said: "We are committed to helping our communities remain resilient and this support will help local councils deal with any immediate and unforeseen costs resulting from the recent heavy snowfalls and ongoing cold weather.
"Although we expect to have seen the worst of the severe weather, we're aware there remains a flooding risk in some areas as the snow melts.
"The Scottish government has been holding regular meetings of the Scottish government's Resilience Room (SGoRR) to monitor the situation and I would urge people continue to take care and to check for the latest guidance from Police Scotland throughout the day."
Local authority umbrella body Cosla said it was "good to see that the Scottish government has responded so quickly and so positively".
Cosla president Alison Evison added: "Financial support for councils who have been worse hit by recent weather events and for those councils who are at most risk from flooding as the snow melts will be crucial, given the challenges already facing council budgets.
"This is how partnership working between the two spheres of government should work and it is good to see it in action.
"There must be a continued constructive dialogue to ensure that the necessary financing is always in place so that local councils can get on with delivering essential services and paying their staff appropriately whatever the weather throws at us."