This is the way I see it:
Since your examples are sentences that would rarely (or never) be said by anyone, it’s tricky to explain the difference.
Do you mean “someone” or “anyone”? I assume you mean “anyone”, otherwise I have difficulty making sense of your sentences.
I would say that it depends on who says it and on the context.
If it was someone who had power over you who said it and you had to follow their orders, there would be no difference - in my opinion.
If you said it to me, “mustn’t” could also mean “shouldn’t”, in which case you’re expressing your opinion about what you think I ought to not do.
If you said “aren’t to” I would assume you were referring to a rule or law that dictates I’m not allowed to cheer people up.