My daughter bit her fingernails when she was three. I told her if she stopped I would paint her nails. That was incentive enough, and she stopped. When she was almost 5, she started full day school and started chewing again. I couldn't find anything to inspire her to stop until her three year old brother started biting his nails. She decided on her own that he had copied her and she felt bad, so she stopped chewing. Unfortunately, this did not influence her brother to stop, and I don't know what his motivation might be.
I think there is a lot of pressure on three year old children. They are no longer babies but don't have the skills to do what the older kids can and they are frustrated. In addition, they are feeling pressure to be big kids and not have potty accidents, behave, and even start classes sometimes. It's enough to make anyone seek an outlet. I wouldn't recommend punishments or aversion therapy like bad tasting spray. I would wait for a time when stress is lower, when she won't need the behavior as much, then give her incentives and positive reinforcement to quit. I think I would start with the toes first because they are easier to keep inaccessible by keeping shoes on or wearing slippers or even better footy pajamas. Once she has stopped that you might be able to find inspiration to stop fingernail biting, if not, at least that habit is not quite as nasty.