Cute usually refers to appearance: babies are cute, dogs are cute, some people are cute. Nice often refers to how a person acts: it means he or she is kind and not mean. Nice can also mean “good quality”: that’s a nice car; she has a nice house. Sweet also usually refers to how a person acts: it is similar to “nice,” but a little bit stronger. A lot of people are nice, but fewer are so nice that they deserve to be called “sweet.” Of course, sweet can also mean sweet-tasting, like sugar.

They are mostly used as compliments. I can say you have a cute dog, a nice voice and so on...