Terry was cleared in court of racially abusing Ferdinand's brother, Queens Park Rangers defender Anton, while playing for Chelsea in a Premier League match last October.
Cole, who is black like the Ferdinands, appeared in court as a defence witness earlier this month. A day after the verdict, Rio Ferdinand appeared to endorse a tweet describing Cole as a "choc ice," a slang term perceived as meaning black on the outside and white on the inside.
Ferdinand tweeted: "I hear you fella! Choc ice is classic hahahahahaha!!"
Ferdinand later tweeted that it was "not a racist term. It's a type of slang/term used by many for someone who is being fake."
Cole said he didn't plan to complain. But Ferdinand, a former England captain, is now facing a fine or ban after being charged by the FA.
"The allegation is that the player acted in a way which was improper and/or brought the game into disrepute by making comments which included a reference to ethnic origin and/or colour and/or race," the FA said in a statement.
Ferdinand failed to make England's squad for the European Championship squad in June and July, even after several defenders were ruled out because of injury. He has until Thursday to respond to the charge.
Terry is also the subject of an FA investigation after being charged by the governing body over the racism allegations he was cleared of at Westminster Magistrates' Court earlier this month.
Terry denies the charge, saying he only used the offensive term sarcastically to counter the profanity he claims Ferdinand was accusing him of using.
In a separate football racism case on Monday, an employment tribunal ruled that a black footballer was unfairly fired by fourth-tier club Gillingham after being racially victimized.
Former Barbados international player Mark McCammon took legal action against the club after being dismissed for alleged misconduct last year.
McCammon claimed black players at the club were treated differently from white players. He said he was ordered to come into the club's ground when it was snowing and driving conditions were treacherous while some white players were told they weren't required to attend.
He also told the tribunal that the southeast England club refused to pay private medical bills to help him regain fitness following an injury. By contrast, he said a white teammate was flown to Dubai for treatment at the club's expense.
"Today we have received the decision of the Ashford Employment Tribunal, which sets out their findings that Mark McCammon was unfairly dismissed and that his dismissal was an act of racial victimization," Gillingham said in a statement. "We are hugely disappointed, in fact staggered, by this decision."