Unless I missed it big-time, I didn't see you mention the instructor at all. That seems like an important omission. Did you talk with the instructor about what you should do next time? Did the instructor seem irritated that you were out there with your son? Did the instructor make any announcements to parents, before class began, about whether or not to do that, or whether they were welcome to stay or go? I would think, since this was the first session, the instructor should have talked to the parents briefly as a group just to introduce how the class would work. I'd talk with the instructor if you haven't already done so. If he or she has much experience with kids this age, the instructor should be able to handle the class and encouage kids (if the class is not too large -- how big is it? Did your son perhaps feel overwhelmed because there were lots of kids?).
As for deepening his dependency or making him more afraid by going out there this time -- no. He's only three. If he were five or six and still this reluctant, then I'd say you need to work with him on separating. But at three, some kids are very gung-ho about dashing away from mom right into a group of stranger-kids, while other kids still want to hang back, assess what's going on, and be led more than taking the lead themselves. It's just fine! He will not be clinging to you on that first day at school in three years' time if you give him confidence now, and showing him it's OK to go out there and participate was giving him confidence the way he needed it. Within a few classes he may well be showing off for you how eagerly he heads for the activities. If he's not, you might consider whether the class itself was right for him (too big, too noisy, expected too much, expected too little, instructor wasn't engaged well with the kids). But that issue would be with the class-- not him and not you either.
