Arnold, 49, who steered Central Coast Mariners to the A-League title last season, called the Blades "prehistoric" after claiming he had turned down an approach for the vacant manager's position at Bramall Lane.
The former Australia coach told The Australian newspaper that he had been interviewed for the Blades job via a video call and had no hesitation in turning the job down.
Winter, who returned for a second spell as chief executive at Bramall Lane last month, told the club's official website: "While Graham Arnold may have been responding to one or two challenging questions, I'm flabbergasted and disappointed by his remarks, which are unprofessional, clearly misinformed and not the actual position of the club.
"Key information about how the club is structured and how it plans to operate has been clearly missed.
"We set out a clear manager profile to meet the future needs of the club to 'act differently' in terms of player recruitment and continue the utilisation of home-grown talent where the club has been incredibly successful in recent years."
Winter added that the Blades, who sacked former boss Danny Wilson with five games of the regular season remaining and replaced him with coach Chris Morgan, were still holding interviews and would soon be in a position to choose from a short-list.
"We have still got some more interviews and will then look to appoint from the strong line-up of candidates," he added.
Port Vale coach Robert Page, a former Blades defender, ex-Blackpool and Portsmouth boss Michael Appleton and Wally Downes are all reported to be still in the frame.