Today is 1 June. Many people in Australia consider today to be the first day of winter. Surely it is cold…
In modern Japanese, June is called 六月（ろくがつ）, but the old name for June is 水無月（みなづき、みなつき）. 梅雨（つゆ）, the rainy season, starts in June, so I always wondered why it is called “no water month” but apparently this 無 is the same as the modern particle “の”, thus 水無月 simply means水の月, "the month of water."
It not only rains a lot in June in Japan, it requires a lot of water for 田植え（たうえ）, rice planting. So "the month of water" sounds like an appropriate name.
By the way, yesterday was still May, 五月（ごがつ）. The old name for May is 皐月（さつき）.
Have you watched a Ghibli movie called “My Neighbor Totoro”（となりのトトロ）? If you have, you may remember that the two main girls in the movie are called さつき and めい. Even though the movie does not mention it, I believe they were both born in May!