SR4A p.326 (emphasis mine) :
Clothing and Armor
No one wants to walk the streets naked—not just because of the social
implications, but also because of everyday dangers like acid rain and
ultraviolet radiation.
Every single bit a fluff in the books describe Seattle as rainy : there is 21 occurences of "rain" or "rainy" just in SR4A, and 14 more in the Seattle 2072 add-on (with 4 occurences of "acid rain" !). Smog and bad air come also regularly.
SR5 has less resources but is consistent, p.436 :
Clothing and Armor
In 2075, you’d have to be crazy to consider walking
outside with just a tee-shirt and jeans, even in some
of the nicer parts of the Sprawl. You need protection:
from the acid rain, from air pollution, from ultraviolet
radiation from the completely fragged ozone layer, and
of course, from random street violence.
So I guess 2070-Seattle is as bladerunneresque as can be.
EDIT : found additional (in-game) informations, Seattle 2072 p.9 :
Annual precipitation is actually around 90 centimeters, [...] It rains more in the winter months, less in the summer. Rainstorms are shorter in the
warmer months and longer in the winter.
Average annual temperature is around 21° C, up to 31° C in the summer, and down to around 4.5° C in the winter. Winter temperatures rarely drop below freezing and weather is usually mild, with occasional thunderstorms during spring and summer and windstorms in autumn.
Due to eruptions from Mt. Rainier, southern parts of the metroplex
often experience significant ashfall, and deposits of volcanic ash
are frequently disturbed by high winds.
Ocean winds tend to improve air quality in downtown Seattle, which suffers from fewer stage-one smog alerts than any other major UCAS city.