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No, but thermodynamics tells us something. A football has a high surface area to mass ratio, meaning it doesn't take much for a ball to lose it's heat, and as the leather represents 99.9% of the mass of a football (one extra atmosphere of air doesn't weigh much), we can infer that a football that feels cold to the touch has more or less reached it's equilibrium.
I wouldn't assume that. Just because the very surface of the ball feels cold doesn't mean the cold (or lack of heat, to be more precise) has worked through to the inside surface of the leather, let alone chilled the air. Plus, the air is in a bladder that the leather is sewn around, as I understand it. Any air in the space between the inside of the leather and the outside of the bladder will act as an insulator, further slowing the time between when the outside of the ball feels cold and when the air inside has reached equilibrium with the ambient temp.