Yes

you do need a jacket based on the weather in Madison, WI, USA 1 second ago

Why? Because you're not freezing, but you’ll definitely start complaining if it lasts much longer and it's so windy, your hat will probably launch into orbit!
37°F3°C & Windy

Wind is 16 mph25 km/h from the Southeast, gusting to 30 mph48 km/h
April 2
1am38°F3°C17 mph27 km/h SoutheastDrizzle
2am38°F3°C19 mph30 km/h SoutheastWindy
3am38°F3°C20 mph32 km/h SoutheastWindy
4am37°F3°C20 mph32 km/h SoutheastDrizzle
5am36°F2°C21 mph33 km/h SoutheastRain
6am36°F2°C20 mph33 km/h SoutheastRain
7am35°F2°C19 mph30 km/h SoutheastRain
8am35°F2°C21 mph34 km/h EastRain
9am36°F2°C22 mph36 km/h SoutheastRain
10am37°F3°C22 mph35 km/h SoutheastRain
11am38°F3°C18 mph29 km/h SoutheastRain
12pm39°F4°C18 mph29 km/h SoutheastRain
DateLowHighWindDayNight
April 127°F-3°C42°F5°C10 mph16 km/h from SoutheastMostly CloudyRain
April 235°F2°C65°F18°C19 mph30 km/h from SoutheastRainWindy
April 338°F3°C50°F10°C14 mph23 km/h from WestMostly CloudyPartly Cloudy
April 433°F1°C51°F11°C8 mph13 km/h from EastMostly CloudyDrizzle
April 537°F3°C50°F10°C12 mph19 km/h from NorthCloudyMostly Cloudy
April 633°F0°C45°F7°C10 mph16 km/h from NorthwestMostly CloudyMostly Cloudy
April 727°F-3°C37°F3°C11 mph18 km/h from NorthwestMostly CloudyMostly Clear

Yes

Low of 35°F2°C, High of 65°F19°C
Wind: 19 mph30 km/h
Precipitation: 95% rain

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