Laws vary from place to place, so in order to know for sure, you will have to contact authorities in your area. However, the general consensus would undoubtedly be yes. The reason is, an e-mail that blatantly states that you will do something in return for something else is a legal agreement.
Even though laws differ, the general principles remain the same: "if two parties enter into an agreement with their eyes wide open, and if the agreement is not egregiously unfair, and if both parties are competent and both parties have signified their understanding and acceptance of the terms", then you have a legal agreement.
A legal agreement, simply put, means that if one party agrees to do something in return for something else, both parties are obligated to fulfill their duties. The problem usually arises when one party doesn't.
Bottom Line:
Yes, e-mails will most probably be legally binding in your country. However, if we can advise you, rather get a proper contract in place for big projects. We use contracts and it really does make a difference, even if it's just for clarity on things you wouldn't normally have thought of.