Born and raised in Philadelphia, he entered the first class of the Curtis Institute of Music in 1924 as a pupil of Felix Salmond and graduated in 1934. Along with Jascha Brodsky, Charles Jaffe, and Max Aronoff, he was a founding member of what was then known as the Swastika Quartet, in 1927. When Hitler came to power and adopted this symbol of Apollo (albeit rotated), the fledgling quartet needed a new name and, with the permission of the school's founder, Mary Louise Curtis, they were granted the name of their alma mater. The Curtis Quartet was a pioneer in its time, being the premier group in America during the prewar years and the first American quartet to tour Europe, including a command performance before Mary of Teck, Queen Consort of George V of the United Kingdom. Before disbanding in 1981, the founding nucleus of Brodsky, Aronoff, and Cole remained intact; after Jaffe, the second violin position was held by Louis Berman, Enrique Serratos, Mehli Mehta, Geoffrey Michaels, and Yumi Ninomiya Scott.
During all this time, Cole was as well close with his classmate and friend, Samuel Barber, who first wrote for him the sonata, op. 6. They in fact collaborated on it as students, with Barber writing a page at a time which the two would read through together, until they gave the work its premier in Town Hall in 1934. Barber wrote as well his quartet, op. 11, with its famous adagio, for the Curtis Quartet. Incidentally, the ensemble played this work from manuscript for several years, and it was only when the time of publication arrived that Barber chose to make major changes: the first movement was cut down significantly, with its finale ultimately becoming the finale of what we have now as the third movement; and the original contrapuntal third movement was abandoned entirely for a reprise of the first movement material. In addition, the work Dover Beach, for baritone and quartet, was written for them. This work was originally conceived for mezzo soprano, but after hearing the premiere in Curtis Hall, Barber was dissatisfied and chose to sing it himself for the subsequent recording made with the Curtis Quartet.
Cole has taught at the Curtis Institute of Music for seventy-five years, first as Salmond's assistant while still a student and then succeeding his teacher. There was a brief gap in his tenure at the school, however, during the years just following World War II. The members of the quartet had grown dissatisfied with certain of the objectives and policies of the school and decided to found their own institution for the training of chamber and orchestral musicians, called the New School of Music. This institution, initially located just a few blocks from Curtis, was for over thirty years an important training center. After returning to their duties at Curtis in the mid-1950s, Cole and the members of the quartet taught concurrently at both schools. Not long after the ensemble's violist, Max Aronoff, who was also director of the New School, died in 1981, the school was absorbed into Temple University where Cole and Brodsky continued to teach. Cole also helped to found the Encore School for Strings in Hudson, Ohio, along with David Cerone who had left his position as violin teacher at Curtis to assume the directorship of the Cleveland Institute of Music. During nearly all this time, he has worked with his former pupil and assistant, Metta Watts. .
Cole has held master-classes all over the world. As of 2008 he was retired from the Curtis Institute, but continued to teach at the Temple University in the preparatory division with his assistant Metta Watts. Cole presently resides in Philadelphia.