"It's snowing outside. Don't go out and play."
别 - suitable in the command form
没 - used when describing action that is not done. Some special exceptions are 能, 可以, 要
不 - to negate action that one does not want to do or intend to do
别 is the imperative "do not" is this context. 不 and 没 alone are not generally imperative. They are more like "(is/does) not." However, the phrase 不要 is pretty similar to 别 and could probably be used here.
The short answer: 别 means "don't" (when giving a command) and 不 means "not" (in general). 没有 means "not have", and is always used instead of 不 with 有. See: https://resources.allsetlearning.com/chinese/grammar/Negative_commands_with_"bie" and https://resources.allsetlearning.com/chinese/grammar/Comparing_"bu"and"mei"
They are not imperatives. 别 means "do not" here. 不 and 没 are more like "(is/does) not." However, 不要 would be similar in meaning to 别 in this context.
It's "don't do something", as opposed to mei "hasn't done sth" and bu "not". In other words, it's asking someone not to do something.
别 is used to express a sort of command not to do something. As in "dont speak english" 别说英语
没 is a short form of 没有 usually used to negate past forms,
不 Negates present forms
别 Is sort of a command order like Shut Up! 别说！
They're just different words. 别 Is similar to stop, 不 is like no, and you couldnt possibly use 没 in this situation. It's one of those things you figure out with more time and practice.