In a statement, the principal Honor Irvine described him as a "special little boy".
"Thomas was a beautiful, much-loved child who added a great deal to the lives of all he touched here in the primary school.
"He loved life and lit up the classroom with his beautiful smile.
"Although we, as a school family, are deeply hurt by the loss of Thomas, our thoughts, prayers and sincerest condolences are with the whole family at this time."
The boy's scout group paid tribute to him.
The Colebrooke and Coonen Scout Group said: "We are absolutely dumbfounded and shocked to hear the tragic news of losing one of our members.
"We want to express our deepest sympathy to the family of our little squirrel, Thomas, who was taken from us tragically in a farm accident. He was the one with the smile to melt a heart and the glint in the eye to add the spark.
"He will be deeply missed by all his fellow squirrels and indeed all the scouting members and leaders."
Victor Warrington, an Ulster Unionist councillor and family friend said the news of his death has sent shockwaves across the local area, particularly the farming community.
"The news is devastating and tragic and everyone's thoughts and prayers are with the family at this time," he said.
"I have been talking to quite a number of people in the area and everyone is in total shock and disbelief. It's a close-knit farming community and we all know each other in some way. I know David quite well and I have been at the farm on a number of occasions."
One neighbour, who did not want to be named, said the family moved to the farm around two years ago.
DUP leader Arlene Foster and Assembly member for the area expressed sympathy. "The family will be in my thoughts and prayers today and in the weeks to come, as they mourn the loss of a young life taken under such tragic circumstances," she said.
Ulster Unionist Tom Elliott also expressed his sadness.
The Fermanagh and South Tyrone MP said: "This is a highly respected and hardworking family, who I am sure are devastated at this very difficult time. As a farmer and parent myself, I am only too aware of the dangers on a farm. No-one ever thinks these accidents will happen and all I can do at this time is to offer the family my sympathy and support in the aftermath of this tragedy."
Sinn Fein MLA Michelle Gildernew said the community of Maguiresbridge was "devastated".
In a statement, the Health and Safety Executive confirmed it is investigating the farm fatality.