If a man texts his ex swearing at her and criticizing her for breaking up with him in an immature way, is this cyberbullying?

It may be cyber bullying but the question is does it rise to harassment. If it is just one text it does not constitute harassment. Sometimes people are upset with you and they just tell you.

It may be, but the question under NY law is whether it constitutes a crime or not. The definition of harassment is "He or she engages in a course of conduct or repeatedly commits acts which alarm or seriously annoy such other person and which serve no legitimate purpose." Thus, if it was only 1 text, it's unlikely to fit the definition. Schedule a consult with a Westchester Domestic Violence attorney for a full assessment.