The vast majority of "copper coloured nickels" out there, are coppery in appearance because of environmental staining - they were buried in damp soil for some time, and the humic acid in the soil has imparted a brownish tone to the coin, giving an overall coppery appearance. Or they've been sitting in a chlorinated pool or fountain, and the chlorine has done much the same thing.
What it's not going to be is some kind of "wrong metal" mint error - especially if it's so heavily circulated that the date has worn away. If it's that well worn, it must have been handled by many, many people for several decades - and surely at least one of those people would have noticed if it was coppery in colour, and put it aside rather than spend it. Especially if it had been bright shiny red-as-a-cent coppery when it left the mint. So, logically, the "copperization" of this coin happened after it became heavily circulated.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis