Devon County Council says a prolonged cold spell could cause further deterioration on local roads - it is already reported to have a£215m backlog of repairs.
"At low temperatures the road surface can become stiffer and can result in cracking, forming potholes," a spokesman told the thisisexeter website.
"Devon spends around£7m a year on patching works - with over£2m of this on reactive safety work such as pothole repairs.
"The additional reactive maintenance that may be required due to the weather could cost an extra£2m above the normal budget spending."
Margaret Rogers, the county's executive member for environment, said: "It is too early to predict the scale of damage caused by this prolonged cold spell but it could double the demand for reactive maintenance over the coming months.
"Reactive repairs have little effect on reducing the maintenance backlog but are necessary to keep roads in a safe condition."
In the past three months, gritters have turned out on Devon's roads on 68 occasions, using 8,800 tonnes of salt at a cost of£515,000 - equalling last year's total figure for the whole winter.