Thompson had no argument with referee Steven McLean's view that the pitch was unplayable when his original inspection was made at 10am.
The SPL and SFA then allowed the Tangerines' staff and volunteers a further hour to work on the surface and they managed to clear 80% of the ice.
However, with the Accies squad due to leave for Tannadice at 11am, McLean called the match off. Thompson, one of those helping to clear the park, was unhappy at the perceived inflexibility of the authorities and argued that a noon inspection would have seen the game given the go-ahead.
"There was still a patch of ice on the park in front of the Shed at 10am but by 11 we had removed 80% of it and as I look out now, just after 12 o'clock, the pitch is perfectly playable," said Thompson.
"I don't want to have a go at the referee because he was told that he had to make a decision by 11am and that was final. He had to make a decision as he saw it there and then. At that point the pitch wasn't playable because of a very small patch of ice sitting on top of the grass.
"But if they had given us another 45 minutes or so the game would have gone ahead. Someone decided that 11am was the cut-off point and, frankly, I think that is nonsense. It is ridiculous.
"By 3pm the pitch would have been fine — I am absolutely sure of it."
The Tangerines suffered more than most with the weather, having lost home matches against Rangers twice, Motherwell and now the Accies game.
Criticism
Some fans, frustrated at not seeing their team at Tannadice since November 13, when they drew with Kilmarnock, have been criticising the club.
However, Thompson argues that they have done everything they possibly could, even enlisting the help of a contractor last week to clear the streets surrounding the ground.
"We have done everything we can to get the game on," stressed Thompson. "We have had diggers in removing snow from the streets outside and the staff have been working on the pitch.
"I don't think people realise how much effort has gone into trying to beat the weather recently. We have not had a home game for about six weeks so that is no income coming in even though wages and other costs still have to be paid.
"We were desperate for the Hamilton game to go ahead and I really want our fans to appreciate that. We were expecting a big crowd and probably about 2500 more than we will get for a midweek game sometime next year."
United director Derek Robertson also stressed that the Tannadice pitch protection had done its job.
"Our undersoil heating was working well," he said. "But it was simply not designed to cope with such sustained sub-zero temperatures. For instance, I was driving into the ground the other day and the temperature gauge in the car was reading minus 12 degrees. We also had the pitch covered but there was still ice forming underneath.
"I attempted to let our supporters know as soon as the ref made his decision but there were so many people trying to access our website it kept crashing and it took me 15 minutes to upload something that would normally take 30 seconds."