The Chelsea full-back been the subject controversy in recent weeks after angrily calling the Football Association a "bunch of twats" following the publication of the written reasons behind John Terry's four-match ban.
"He is a great person, great personality and experienced person," said Hart. "He was very welcoming, especially to myself. I've noticed that with the young lads.
"That's the beauty of him. If you don't know him, you won't know him. When you do, you'll find he's a really welcoming person.
"He's had his issues and he doesn't speak out especially, but to meet him personally he's a great person to know and someone I really admire as a footballer."
Cole, who has 98 caps for England, was charged by the governing body for his comments but has not been suspended from the Three Lions' 2014 World Cup qualifiers against San Marino and Poland this week.