As a native speaker, I have seen and used the phrase "I hope this letter finds you happy and in good health". For some reason "good health and happy" seems more awkward, but i would not find it too strange if a native speaker wrote that to me either. It's a slightly old-fashioned phrase from the days before email. Young people would not say it, unless speaking to an older relative or friend. This phrase is typically at the beginning or the end of the letter.

there is no wrong with it if the letter is to your friends or other intimate people.but if not,u'd better to be more formal.

I hope this letter finds you well.