Yes! I am a musician as well (saxophone mostly) and while there isn't a lot of time for music, a large number of cadets are quite musical and make time for it. There are several pianos in Arnold hall, as well as the chapel. There is also one in the Oasis in Sijan hall. Many cadets have keyboards in their rooms as well.
As for musical opportunities, there was (and hopefully still is) a cadet symphony orchestra that got together for 1.5hrs on Sundays to rehearse and played a few concerts a year. Nothing serious, just a group getting together to play, but we were pretty good because everyone involved was a pretty committed musician with a high level of skill. There is also a show choir with a live band (I was a co-CIC , cadet in charge, for this my senior year) that allowed for a lot of creativity and jamming. We basically came up with our own parts based on 4 part choir charts. A jazz band has been on and off for a while, but it was very cadet run and dependent on the current cadets (it existed my freshman year, but had died by my senior year).
I often just played in my room during odd hours, but there are several rooms in the chapel as well as Arnold hall that can be used for playing. I also occasionally used an empty classroom in Fairchild in the evenings.
In short, yes, there are opportunities and plenty of musically inclined Cadets.