Does this make grammatical sense in Japanese?

Question:

I am attempting to say, "I've heard that Japanese letters begin with (mentions of) the weather."

"Tenki de nihon no tegami wo kakihajimeru soudesu."
てんきでにほんのてがみをかきはじめるそうです

Answer:

It's about 時候の挨拶 jikou no aisatsu), and the sentence should be:
"I've heard that Japanese letters mention SEASONAL thing briefly before the main topic." (NOT always)

ほんぶんの まえに きせつにかんすることに ふれるそうです。
fureru = touch on/mention briefly

weather is translated てんき・てんこう, but we actually write seasonal thing such as
もう　つゆの きせつ と なりました ⇔　そとは あめが ふっています
"We've already been in rainy season" rather than "It's raining outside"

You might know ’Haiku’ usually includes seasonal keyword (= "kigo")

----------- Add: 時候の挨拶 jikou no aisatsu (--> kakidashi = how to begin)
http://www.nengasyotyuu.com/bunrei/zikou…

------ I forgot to write full sentense.
So please add ” にほんでは（or にほんじんは） てがみをかくとき、”
before the sentence "ほんぶんのまえに～"