Harry Sinclair, president of the UFU, said: "There are potentially in excess of 10,000 sheep dead already. And a lot of these sheep that are living could end up with dead lambs.
"It (the cost) could well be £3m.
"There is a lot of structural damage – we have heard of roofs off cattle sheds – and a lot of that is not covered by insurance.
"I would hope it (the cost) does not go any higher than that, but we just do not know at this stage."
Mountain rescue teams, the Red Cross and local workmen have been working day and night to clear roads and airlift supplies to families stranded in their homes since Friday.
On Sunday afternoon, an RAF helicopter dropped vital supplies to the distressed father of a six-week-old baby just outside Co Antrim's Glenarm area.
Hours later, an elderly man was airlifted to hospital after he suffered health complications in his home in the Glenarm area.
Farmers and families are now starting to count their dead animals. Among them is Elaine McGarel. The mother-of-five from the Feystown Road area of Glenarm is picking up the pieces after three days without electricity or running water.
The family has nearly depleted a two-year supply of hay in just three days in the struggle to keep their animals alive at the peak of lambing season.
Elaine cannot account for 50 of the family's 200-strong flock of sheep. "It's totally and utterly soul-destroying; horrendous," she said, indicating a cluster of dead lambs at the side of a farm shed.
On Sunday, Elaine and her children – two of whom have Asperger syndrome – were forced to battle through snow drifts of up to 10 feet, to collect vital supplies of bread, milk, petrol and batteries.
They now face the cost of not only losing a significant proportion of their livelihood, but also paying to dispose of their perished flock.
As Elaine described her devastation, her son rushed off to help a ewe in labour in the snow.
"It's a case of livelihoods being destroyed," Elaine added.
"We tried to be prepared for it, but we were not given the right warning. We need help here."
Harry Sinclair described the mood among farmers as "depressing".
With farming incomes cut by 50% across Northern Ireland last year, farmers had been hoping for an early spring.
Campbell Tweed, who has more than 2,000 ewes on his farm just outside Cairncastle near Larne, spent Monday scouring the hills for missing animals.
"I have absolutely no idea what the scale of what we have lost is, because it is all buried under the snow," he said, standing beside a scattering of sheep which had suffocated under the weight of snow as they sought refuge.
Agriculture Minister Michelle O'Neill visited the area on Monday and promised to muster help for farmers.
She said: "I have asked that all resources available to the Executive, including those of the emergency services, are made available to help those affected.
"Farmers experiencing problems should call their normal contact within the department or alternatively the DARD Helpline on 0300 200 7852."