Yes

you do need a jacket based on the weather in Cortland, NY 13045, USA 1 second ago

Why? Because it's drizzling and it's cool enough your breath is visible, but your nose isn’t red yet and it's super windy outside!
37°F3°C & Drizzle

Wind is 11 mph18 km/h from the Southeast, gusting to 27 mph44 km/h
April 10
10pm37°F3°C12 mph19 km/h SouthRain
11pm36°F2°C13 mph20 km/h SouthCloudy
April 11
12am35°F2°C12 mph20 km/h SouthCloudy
1am35°F2°C11 mph18 km/h SoutheastCloudy
2am35°F2°C10 mph16 km/h SoutheastCloudy
3am35°F1°C10 mph16 km/h SoutheastCloudy
4am34°F1°C10 mph17 km/h SoutheastCloudy
5am34°F1°C10 mph16 km/h SoutheastCloudy
6am35°F1°C10 mph16 km/h SoutheastCloudy
7am35°F2°C10 mph16 km/h SoutheastCloudy
8am36°F2°C10 mph17 km/h SoutheastCloudy
9am38°F3°C11 mph17 km/h SoutheastDrizzle
DateLowHighWindDayNight
April 1026°F-3°C40°F4°C7 mph12 km/h from SoutheastRainRain
April 1134°F1°C45°F7°C8 mph14 km/h from SoutheastDrizzleCloudy
April 1236°F2°C45°F7°C7 mph11 km/h from NortheastDrizzleMostly Cloudy
April 1336°F2°C50°F10°C8 mph13 km/h from NorthMostly CloudyMostly Cloudy
April 1436°F2°C59°F15°C9 mph14 km/h from SouthMostly CloudyRain
April 1531°F-1°C47°F8°C15 mph24 km/h from WestDrizzleSnow
April 1627°F-3°C38°F4°C17 mph28 km/h from NorthwestWindyMostly Clear

Yes

Low of 35°F2°C, High of 46°F8°C
Wind: 8 mph14 km/h
Precipitation: 50% rain

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