Video warning: The report contains some distressing images.
Carcasses will be collected by firms approved by the Department of Agriculture and Rural Development (DARD) until Monday 15 April.
The collection deadline may be extended depending on the speed of the thaw, the department has advised.
Counties Antrim and Down were worst affected with snow drifts of up to 18ft in some areas after gale force winds and heavy snow fell almost two weeks ago.
Sam Abbott was in Castlewellan in Co Down working to collect animals that had perished in the freezing conditions.
He said it was heartbreaking to see so many dead lambs and ewes.
"The farmers in the mountains have got a raw deal," he said.
"Today has been a very hectic day for the first day the collection, the phone hasn't stopped ringing today, (we've) been inundated and we're just trying our best to get the stock off the mountain for the farmers.
"It's out of sight, out of mind."
Terry White is a farmer in the area who lost around 40 lambs in the adverse weather.
"We couldn't get near our hill sheep for four days because the road was blocked, we had trouble getting them home, whenever we got to the mountain, the ewes had lambed early, walked off and left their lambs, it was just a disaster," he explained.
He said his fields had only thawed slightly, and were still covered in snow over a week after the blizzards hit.
It's not easy, when you see your year's work going away in a lorry when it should be going to a meat plant or market, it's soul-destroying.
Terry White, Co Down farmer
Farmers in areas eligible for the collection service are to contact the Rendering Plants 'Linergy Dungannon' on 028 8775 0050 or 'Foyle Proteins' on 028 7186 1120 to arrange removal of the carcasses.
At present, the following postcode areas are eligible for collection - BT25, BT31, BT33, BT34, BT35, BT36, BT40, BT43, BT44, BT54. However, the list is subject to change and farmers should check DARD's website.
"Farmers should NOT contact DARD to arrange collection of fallen stock," a statement from the department said.
"Farmers should move fallen stock to a point on the farm which has hard standing (concrete or tarmac) and which the collecting vehicle will be able to access (central yard, end of farm lane, etc)," the department advised.
A number of carcasses may be moved to this point, and all carcasses must be covered with a tarpaulin or similar so that it is not possible for dogs / foxes / birds to access them until they are collected, the statement continued.
Carcasses must be held securely in this way until removal.
"DARD will verify the losses of animals by supervising collections of animals. Animals collected without verification by DARD staff will not be eligible," the statement continued.
Meanwhile, the public is being advised not to approach or touch the dead animals.
"Do not allow other animals (ie pet dogs) to approach or touch the dead animals," it was also advised.
Anyone who finds a dead animal should contact the DARD helpline on 0300 200 7852 with details of the dead animal - the species, number of animals and location.