Dear Erin,
You are describing my own son at age 3 exactly. At that age, N. was verbal, confident, and funny with family members, but if you put him into any situation with other children, or what I'd describe as even mild chaos, he'd just withdraw to the point of being a silent little lump. We had all kinds of possible diagnoses (autism, developmental delays, you name it) suggested to us.
Today, at 4 and a half, N. is an amazingly happy, confident little boy. He has two best friends, from whom he is inseparable, but he'll play with just about any child at his preschool. He's also extraordinarily confident on things like playground equipment, though FWIW, he seems distinctly less athletic than other kids his age.
What produced this magical, unbelievable transformation? Three things: Playdates, Montessori, and time.
It seems to me that your son already has the one key ingredient to coming out of his shell, and that's friends he will play with. What I really, really recommend is inviting these kids over for playdates *as much as possible.* Sign him up for activities *with* these friends. With N., once it was clear that he was forming a real friendship, I basically had to struggle against my own shyness, explain the situation to this boy's M., and ask for her help. She turned out to be fine with it, and she and I are now good friends too.
I also wonder if your son is at the right preschool. When N was 2, I signed him for a few mornings a week at a very simple, local co-op preschool. Mistake. The place seemed sweet and lovely to me, but it was much too chaotic and unstructured for him. What *has* worked is a Montessori school, where things are very calm and peaceful, and there's plenty of structure. Not only is N. thriving socially there, but he's also doing really well academically: he's already reading and doing addition and subtraction!
Finally, if someone could have told me that N. would have simply outgrown the worst of his shyness -- wow! All these gray hairs on my head wouldn't be there, I'm sure. Three is really young -- kids have their core personalities, but they don't have their coping skills yet. If you support your son, and don't make him feel bad for being shy, I'm really confident that he'll find a way to integrate himself into the world. If my son did, any child can.