Cote was a standout pitcher on the Crusader baseball team from 1954-1956. During his senior year, he earned first team All-New England honors after posting an 8-2 record with a 2.29 earned run average and 77 strikeouts. Cote also had an outstanding season as a junior, when he was 5-3 with a 1.34 earned run average and 67 strikeouts, while in his sophomore year he posted a 4-0 mark with a 1.13 earned run average and 38 strikeouts. He helped lead Holy Cross to a 44-10 overall record during his three seasons on the varsity squad, with the Crusaders advancing to the NCAA Tournament in both 1954 and 1955. In the final game of his collegiate career, Cote threw a one-hit shutout in a 12-0 victory over Boston College, with the only hit he allowed coming on a scratch single with two outs in the ninth inning. Over the course of his Holy Cross career, Cote posted an overall record of 17-5 with a 1.70 earned run average and 182 strikeouts.