In with time expressions is used when you are saying after a specific interval of time, something will happen (i.e. In two hours, I'm leaving.)
If you want to say something is happening at a certain time of day (or certain day of the week, certain day of the month, etc.) use on (except for clock time, use at).
So 4 is wrong.
Now given:
It was raining most days.
It was raining most mornings.
An adverb can be preceded with most, and many times adverbs/adverbial phrases can be flexible where they appear in the sentence, with some positions usually perferred over others:
I flawlessly attacked the enemy.
I attacked the enemy most flawlessly.
So I think here "most days" or "most mornings" works as adverbial phrase that modifies was raining - especially since adverbial phrases can be moved and something like Most days it was raining still means the same thing.
So you can omit the preposition or keep it, the meaning is pretty much the same.