In short... the summers are hot and dry, the winters are cold and wet, the autumns are cold and dry, and the springs are usually a mix. Probably the most important thing to remember about the Portland area though, is that our weather is overall very mild. Like in winter we usually only get snow once a year, and when we do it's only an inch or so. During summer, 80's are a fairly typical daytime high with 50's at night. And yes, as for rain intensity it is usually just foggy and very light rain. We do not get thunderstorms like the gulf coast or Midwest gets (I have lived in Florida).
I Personally have lived all over the country and have found the Pacific Northwest to be by far my favorite area. I can't quite emphasize enough how different and unique each season is around here... that alone is perhaps the greatest (of the many) changes from Florida.
Also, as someone who has both allergies and asthma, I can tell you that there really isn't much to worry about. As I said, spring and winter can get very humid but it's something that you adjust fairly quickly to. We don't have a lot of the large (mostly coal fired) pollution that most of the country does so we have excellent air quality. Admittedly, the time of year when the rains begin to return (around now) can bring congestion... nothing unmanageable.