Usually when you use set in it means something usually negative has come. For example, "The rain has set in." means that a rain has come. But not is a pleasant way.

Technically you could, but as Eli Cieslak said using "to set in" usually indicates something negative. Normally one would say; "The sun has come out.", "The weather cleared up.", "It's sunny". Also to say something like "The sun has set in." sounds old-fashioned.

Just a quick note: "May I say...?" means "Do I have permission?" We understand what you mean, but the natural question is, "Can I say...?", which means "Is it possible/correct to say...?"

Thanks for the answers!)