This is the 12021st most frequent Russian word.
зимнее
"Зимнее" means "winter" or "related to winter" in English.
The word "зимнее" here is the neuter adjective describing "пальто" (coat), indicating that the coat is suitable for or related to winter.
Мы собираемся купить зимнее пальто.
We are planning to buy a winter coat.
The word "зимнего" here is the genitive masculine adjective modifying "сезона" (season), showing possession or association of the season with winter.
Во время зимнего сезона трафик ухудшается.
During the winter season, traffic gets worse.
The word "зимние" here is the plural adjective describing "виды спорта" (sports types), indicating these sports are associated with or performed during winter.