Marimara, my child is like yours, and just a little bit older, so this story might interest you. Last summer I pulled her out of the swimming pool because going into the "age appropriate" 3-6yo class with a teacher and three other kids simply terrified her. I was mad at the parks district for setting the cutoff for parent-child classes at 36 months - you could literally look into every corner of the shallow pool and see crying three-year-olds too frightened to do anything but sit on the steps (as well as other kids who were out in the water doing the things the teacher wanted them too). After talking to parks district, it turned out that we could get a waiver to go back into the parent-child swimming class... and there were more than a few kids her age in there.
But here's the thing - she really wanted to learn to ice skate - a lot - and I couldn't take her, because I can't skate. So she asked for lessons. The first time I enrolled her in a session last spring, she tried to go out there but was just too frightened of her teacher. After a few minutes, a very child friendly and sympathetic teacher at the rink gave her a private lesson, which got her up on her feet at least. She skated holding her dad's hand all summer. About four months later, in the fall, she asked for lessons again, and I enrolled her in another session. At the first class, I told her that she didn't have to go, but if she did, I would give her a chocolate bar (for what it's worth, I don't remember ever bribing her before, and sweets are part of her life - not forbidden fruit).
She went out there, cried for about two minutes, then skated and had a ball. Since then, she's been to a dozen lessons, with zero tears or fears. She always looks to see if I'm there watching her, but she is as confident as she can be, and she loves it. She asked for another treat at the second lesson, but she didn't get one - it was a one-time only thing. Generally, after her lesson, she will skate at least one time around the public sesson oval ALL BY HERSELF, after the other kids have gone off the ice. She is still three - just a more mature three.
So, at the end of this long story I guess I just wanted to say three things:
1) whoever thinks all kids are ready for separate classes as soon as they turn three probably doesn't understand the variations both in kid's personalities and in this stage of development;
2) whoever is offering classes might be willing to waive the age limit, as long as your daughter is not too far over it,
and
3) if the activity is something your daughter really really really wants to do, a one-time bribe might give her the little extra push to get over the hurdle. I know that philosophically some people will want to batter and fry me for that, but to me, it was worth it. She loves to skate, and she can.