All of this made me think of McGill. It has an excellent music program, and excellent math and engineering programs. Some might claim that it has the best music program in Canada (although some other people from Toronto might argue the point). When my older musically-talented daughter applied (and was accepted), we were told that some of the music professors augment their income by giving music lessons on the side. Apparently taking lessons is relatively common even among students who major in something else. The music library and other music facilities there are excellent. There are multiple concerts of some sort or another every week (or were when we were looking). Given your son’s excellent stats, admissions would be very likely.
I did not mention it in my earlier post because of the “not too cold” request. However, I do not think that it is any colder than Rochester and not much different from CMU. It is also in a very attractive city that has a lot of interesting things to do. While Montreal is majority French speaking, the area around McGill (and Concordia, which is close by) is almost entirely fluently bilingual.