Yes

you do need a jacket based on the weather in Reykjavík, Iceland 1 second ago

Why? Because the drizzle is not enough rain to call it "raining," but enough to make you a little soggy and the cold's there, but it's just a reminder, not an invasion!
44°F7°C & Drizzle

Wind is 11 mph18 km/h from the West, gusting to 18 mph29 km/h
September 9
3am44°F7°C11 mph18 km/h WestDrizzle
4am45°F7°C10 mph17 km/h SouthwestDrizzle
5am46°F8°C10 mph16 km/h SouthwestDrizzle
6am46°F8°C11 mph18 km/h SouthwestDrizzle
7am47°F9°C13 mph21 km/h SouthwestDrizzle
8am48°F9°C14 mph23 km/h SouthwestDrizzle
9am49°F10°C15 mph24 km/h SouthwestDrizzle
10am50°F10°C15 mph24 km/h SouthwestDrizzle
11am50°F10°C15 mph24 km/h SouthwestDrizzle
12pm50°F10°C14 mph22 km/h SouthwestDrizzle
1pm50°F10°C12 mph19 km/h SouthwestDrizzle
2pm49°F10°C11 mph17 km/h SouthwestDrizzle
DateLowHighWindDayNight
September 844°F7°C50°F10°C13 mph20 km/h from SouthwestDrizzleDrizzle
September 945°F7°C53°F11°C7 mph12 km/h from NortheastRainRain
September 1049°F10°C59°F15°C9 mph15 km/h from EastDrizzleDrizzle
September 1147°F8°C58°F15°C7 mph11 km/h from NortheastDrizzleDrizzle
September 1245°F7°C53°F12°C8 mph13 km/h from NorthDrizzleMostly Clear
September 1344°F6°C57°F14°C8 mph12 km/h from NortheastPartly CloudyPartly Cloudy
September 1445°F7°C54°F12°C10 mph16 km/h from NorthPartly CloudyPartly Cloudy

Yes

Low of 45°F7°C, High of 53°F12°C
Wind: 7 mph12 km/h
Precipitation: 70% rain

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