Cole was a notable absentee from a civic reception in the city on Thursday night, with Football Association claiming the Chelsea defender was "resting" sparking fears of a potential injury.
However, Cole felt fit enough to train on Friday morning, although it was expected to be a light session.
Indeed, all 22 members of the England squad - Jermain Defoe remains in England following the death of his father - were present for the session which took place in front of 3,000 invited guests.
Later, the England squad were going to split, with six members, including Wayne Rooney and Joe Hart, due to travel to Auschwitz along with manager Roy Hodgson and FA chairman David Bernstein, with the remainder set for a tour of Oskar Schindler's factory, reinforcing England's commitment to the local area.
The policy is in marked contrast to their stay at the World Cup in South Africa two years ago when England were criticised for adopting an isolationist approach when their training camp and hotel were both at the same remote location in Rustenburg.