Council workers have been advised to set aside holidays to cover absences due to bad weather.
A revised staffing policy for severe weather absences warned East Lothian Council would continue to dock workers' pay if they did not come in.
But it suggested those who lived in rural communities "may wish to consider holding back some of their annual leave for events such as adverse weather".
The council said it "could not pay" staff who did not fulfil contracts.
Councillor Jeremy Findlay, whose ward covers North Berwick coastal communities, told a meeting of the council's cabinet on Tuesday that he had a "moral problem" with staff being penalised because they lived in rural areas.
Raising his concerns about the revised policy, Mr Findlay said: "I have a moral problem with someone who lives in the rural county where roads are under two feet of snow being adversely affected when they are being told by police they should not travel and as a result their wages will be docked."
Red weather warnings
Anger over the way the council handled last year's severe snow storms led councillors to overturn its long-standing policy on absences and agree to pay workers who had been unable to get into work.
Many workers were stunned to be told that while police were warning people to stay at home, the council was continuing with its established policy advising them they would have to take time in lieu or unpaid leave to cover the time they were unable to work during the crisis.
While other local authorities, such as City of Edinburgh Council, took to social media to assure staff they would be paid if they were unable to work during the red weather warnings last March, East Lothian Council repeated its advice that workers should report to work if it was "safe to do so".
Alternatively, they could attend the nearest council office or suitable premises, or work from home or other suitable locations, according to the Local Democracy Reporting Service.
Following a review of its actions, wages were reinstated for those who missed work during red weather warnings and the policy was reviewed.
However, the revised policy, which was approved by the council's cabinet this week, showed little change except adding in advice for rural workers to set aside holidays.
Council leader Willie Innes said he expected that should another "Beast from the East" hit the country, councillors would once again step in to ensure wages were not docked.
He said: "It is impossible to have a policy that pleases everyone.
"Last year members took the decision to pay staff - I would hope if it happened again we would consider making similar commitments."
The cabinet approved the new policy.