Yes, I can definitely feel music. I don't have that sensory capacity some people have, I forget the term, to see colours etc. associated with notes.
I do though definitely feel the melody, the rhythm, everything about the music. Also if I know a piece of music, I can usually identify a tune after hearing about one bar of music. I always, from a young age got very animated, or entranced by music. It always has had a very powerful effect on me. Probably for this reason I was a dancer. Music has the amazing capacity to capture every possible mood, emotion or energy, and it's phenomenal to experience that.
What I loved about dancing was the fact that it is so expressive. This was often very often connected to musical expression. I loved it in my training, we had pianists and percussionists playing in our classes. The training I had as a dancer is also helping me now in learning an instrument again, because I feel the phrasing of the music and know intuitively about the phrasing and timing. I need to understand the rhythm first and then the rest fits into place.