The 57-year-old was trapped under the vehicle at the end of Oldham's Saddleworth Band Contest at 10pm on Friday.
His eight-year-old son was left with severe bruising and a broken tooth and is in hospital.
Mary Rodgers, who is on the contest committee, said: "We are all really shaken up and upset about it."
She added: "We were horrified when we heard the news late last night. It's a tragedy."
Andrew Wilkinson, patron of Brighouse and Rastrick Brass Band, said: "Our band was playing the approach march – we had got half way through it before we were told there had been an incident. It's very tragic.''
Police are appealing for anyone with information to come forward.