Yes, that's "Ice" w/ a capital "I"! An established and often mentioned 'movie connection' to BBM is "The Ice Storm". Y? Because, like BBM, it was directed by award-winning director Ang Lee (1997).
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For more movie connections to Brokeback Mountain, U can go to IMDB's BBM, which has an entire section so designated. The first film connection is "The Ice Storm"!