M.,
As a piano teacher and early childhood music teacher, I can tell you that three is too young to start formal music lessons, unless you have a true musical prodigy, and even then I advise you to wait. Taking up an instrument requires an attention span and level of discipline and commitment not inherent in a three-year-old, who still learns through play. It also requires the ability to keep a steady beat among other skills, which most three-year-olds also lack. Most experts agree that age 7 or 8 is the minimum age for a child to begin formal music lessons. Although I currently have two 5-year-old beginners among my students, they are the exception rather than the rule.
That said, there's no reason not to continue to nurture your son's love of music. If you have a piano or other keyboard instrument at home, encourage him to experiment with it and discover the variety of sounds he can create. If he enjoys singing, encourage him to do so. Sing with him, and don't worry about how you sound. Your voice is the most beautiful sound in the world to your son, and by singing with him (and to him), you become a musical role model.
Let your son play with music right now without expectations or direction. Like all new skills, from walking to potty training, your son will take to piano lessons when he's ready.