It would really depend on what part of the Cold War we're talking about, and what we're measuring.

If we are looking at 1950 or so, the answer is clearly Britain and France. The British Empire was even the third "superpower" when the term was coined, and it and France still had empires and militaries that spanned the globe, albeit both were already in retreat. Both were (and are) nuclear powers, with Britain successfully testing a weapon in 1952 and France in 1960.

If we fast forward to 1990 though, the situation looks different. Britain and France probably still had the biggest military force projection after the US and USSR, but both were much reduced in their influence by this point. In nominal terms, economically they had been displaced by Japan and West Germany, which had become the second and fourth largest economies, respectively (the US was first, and the USSR was third).

In geopolitical terms, the People's Republic of China also deserves some consideration, especially from the 1970s on. It was at this time still a very poor country, and one rocked by political turbulence such as the Cultural Revolution, but as the home of Maoism it provided an alternate pole for communist states and movements to align themselves with, especially after the Sino-Soviet split and the Warsaw Pact's invasion of Czechoslovakia in 1968. The PRC also participated in the Non-Aligned Movement and supported a wide number of anti-colonial movements.

So: It depends what you're looking ar specifically and when, but all of these would be major powers in some form or another.