Thank you for your notes on "haru-ichiban". 

Japan in cherry blossom would be a wonderful thing to see! 

My corrections are highlighted, and suggestions are in blue:

The beginning of the spring in Japan

For now in Japan it is the winter season, but spring will come soon!

Today the wind blew hard.
We say it "haru-ichiban" (the first wind in this season from the south).
"haru" is "spring" , and "ichiban" is "first" in Japanese.
When the wind blows, the temperature rises suddenly.
From next day, most of year the cold comes back, (I am not sure of your intended meaning here.  Perhaps something like "Tomorrow the cold may return for awhile") , but we feel the spring will come before long.

I'm looking forward to seeing cherry blossoms!

Thank you for reading my notebook.

【日本の春の始まり】
日本は現在冬ですが、まもなく春が来るのです。

今日強い風が吹きました。
（その年に初めて吹く南寄りの風）私たちはそれを「春一番」と呼びます。
その風が吹くと、気温は急上昇します。
翌日以降は例年寒さが戻りますが、
私たちは春が近いことを感じます。

桜を見るのが待ち遠しいです。