Speaking at High Barlay near Gatehouse of Fleet, Richard Lochhead said the Scottish Government would give more support to farmers once the scale of the losses to farmers was known but stopped short of outlining what sort of support it would be or how much.
"We are working with the industry to measure the damage caused by the weather to agriculture in south-west Scotland.
"We want to make sure businesses can remain viable and help farms recover. We will make more support available once we understand the scale of the damage.
"It's clear there has been significant economic losses."
He urged banks and landowners to "lend a sympathetic ear", adding it had been a disaster for farmers.
The Scottish Government has already provided £500,000 to help farmers pay for collection of dead animals lost in the snow.
More top news
Emma Jesson brings you Sunday's weather forecast
The Environment Agency has issued a number of flood alerts across Cumbria.
London Mayor Sadiq Khan's comments on Scottish nationalism prompted a fierce response from Scottish First Minister Nicola Sturgeon