first frost of the year
Refers to the first frost of the autumn or winter season, often used in seasonal greetings or weather reports.
We had the first frost of the year this morning.
Hearing news of the first frost, I started preparing for winter.
The first frost of the year fell on the garden this morning.
The first frost of the year was recorded in Hokkaido in mid-October.
It's now the time of year when news of the first frost starts to arrive.
初霜 and 初雪 share the same 初〜 'first of the season' structure, but 初霜 means the first frost while 初雪 means the first snowfall.
tenth lunar month
Compound of 初 (hatsu, 'first') and 霜 (shimo, 'frost').