The rain in Washington state is generally a soft rain, you won't see the sidewalk-scrubbing gully-washers like you get in Florida. But there are a lot of microclimates with their own weather going on. Nobody around here lets the rain stop what they are doing, they have the right outerwear. Just get some waterproof boots, and a long waterproof coat, with a HOOD <- important, then you're good to go out any time.
We get Pacific storms in the winter here, with hurricane-force winds and rain. The rain hits the windows horizontally, and HARD too, it's really wild. It hurts on any exposed skin, if you go out, once I went out in it just for fun and could barely stand up. I had just my face exposed and OUCH.
I have a problem with mold also, it's usually worse in the Fall since we get a lot of rain on the fallen leaves everywhere, and they stay wet. Sometimes it triggers my asthma. It's worth it, though, SO pretty here in the Pacific NW.
Maybe the type of rain that they have there is why I don't remember a lot of rain while we were living there. I will hear the stereotype of constant rain in that area and I don't remember it being that way.
We lived in a ranch style home so no upstairs. We didn't have air conditioning and I don't remember missing it, I don't do well with heat either. I remember the occasional day in the 90s but it didn't stay that warm for long periods of time. I think that is what makes it bad when it stays like that for a long period of time. I think everything, buildings, cement even the ground absorbs the heat and it just keeps building. In time it doesn't even cool off much at night because of all the built up heat. The two years that I lived in that area we didn't have anything like that.