When I hung the laundry out during a break in the rainy season, it already felt like summer.

Literal

Rainy-season [possessive-の] clear-spell [at-に] laundry [object-を] hung-out-[conditional-と] mood [topic-は] already summer was.

梅雨 'rainy season' — the annual June-July monsoon. 晴れ間 'a clear spell/break in the clouds.' 洗濯物を干す 'to hang out laundry.' The と conditional here marks a natural, immediate realization: 'when I did X, I felt Y.' A seasonally evocative, very Japanese moment.