Anyone remember a post-apocalyptic, frozen world film starring, I think, Steve McQueen? Something about lack of resources and "game of death" contest to keep the population down?
I checked Steve McQueen's full film list as an actor on IMDB and didn't seem to be any matches to your description.
May be this? Quintet
Quintet is a post-apocalyptic science fiction film by Robert Altman produced in 1979. It features among others Paul Newman, Brigitte Fossey, Bibi Andersson, Fernando Rey, Vittorio Gassman and Nina Van Pallandt.
The story takes place during a new ice age. The camera tracks a blank, frozen, seemingly deserted tundra until two blurry, distant figures can just be made out.
Essex is unaware that the current Quintet tournament is a fight for the survival of the fittest. Those who are "killed" in game are executed in real life.