Moyes got his first experience of Manchester United's global appeal in Bangkok today as fans turned out in force to welcome their arrival in Thailand at the start of a five-match summer tour.
Even more can be guaranteed at Friday's open training session ahead of Saturday's meeting with the Singha All Stars, which marks the first game of Moyes' reign.
Yet it is not until the Red Devils start the season with a run of five successive live Premier League TV games in the middle of next month that the real assessment of the Scot's work can begin.
And Cole knows Ferguson's shadow will loom large.
"It is a massive act for David Moyes to follow," said Cole. "You are losing the most successful manager in English football history.
"The new manager comes in and everyone says to themselves 'we have a chance now'. That is how I would see it anyway.
"Sir Alex Ferguson is the Godfather of football. When you have a presence like he had, it guarantees you a certain amount of points every season.
"Some people just know how to get that little bit more.
"Sir Alex Ferguson could turn a minute of injury-time into 90 seconds.
"What he said at half-time, full-time or in the media meant something might go his way the following week."
It was an advantage that came out of spending in excess of 26 years in the most pressurised of occupations, experience that rather than shunning, as some might have chosen to, Moyes intends to lean on.
The advantage for United is that they are not alone in ushering a new man to the helm.
"It is going to be a special season because every team has had change," said Cole. "Yet in a way, nothing changes at Manchester United.
"Every season they have to prove why they are the best team. This is just another challenge.
"They may have lost their manager but the players have to say to themselves it wasn't just down to him, it was them as a team.
"I have no doubt David Moyes will do a sterling job. Fingers crossed he will be able to win something as soon as possible."
Cole's presence on the United flight underlines the huge organisation Moyes has joined.
Together with Bryan Robson, Dwight Yorke and Denis Irwin, Cole will attend numerous events on behalf of the club as they either maximise their commercial power or fulfil obligations because of it.
Moyes has impressed so far and one of his first tasks upon arrival, along with Ryan Giggs, was to sign a book of good wishes for the Thai king, who is so revered in the country.
And even Ferguson was not immune from losing out on high-profile targets in the transfer market.
United are still waiting to discover whether Barcelona midfielder Thiago Alcantara has opted to join Bayern Munich instead of complete a switch to the Red Devils that seemed a formality just a couple of days ago.
However, Bayern coach Pep Guardiola has comfirmed his interest in a player he worked with prior to his own exit from the Nou Camp in 2012.
"Yes," Guardiola told reporters in Munich earlier, when asked if he was interested in Thiago. "I don't know what's going to happen. We have to wait. But I know him very well. He is a super super player.
"He can play in three, four or five positions."
And Guardiola has made it clear he is not interested in anyone else.
"It is either Thiago or nothing," he said.
If Thiago goes to Germany as anticipated, Moyes will be left to seek midfield alternatives, knowing another player he has been heavily linked with, PSV Eindhoven's Kevin Strootman is mulling over a switch to Roma.
Luka Modric has been periodically on United's radar, whilst Juventus' Claudio Marchisio has also been mentioned, although both are 27 so neither fit the template that existed until last season's purchase of Robin van Persie.