First of all: there is no perfect season for star gazing. Winter has great dark sky because the sun is deep below the horizon and the air is calm because it is cold. And the cold is exactly what makes you want to go back in after 10 minutes because even with 10 layers of clothing and a thermos full of coffee it gets darn cold very quickly. Even at 5 degrees Celsius. The summer is much better in terms of temperature (you can gaze stars wearing a T-shirt) but the sky is much brighter and the air is less calm so the seeing is worse. Spring and fall are in between.
One thing that makes winter better than summer: you can see the nebula in Orion. Then, again, summer has some nice stuff, too, like M57 and Albireo.
So. Never been to Seattle but I live in the middle of a 6 million people conurbation in Germany. It is possible to observe deep sky objects from here even if it's difficult and the set of visible objects is far smaller than in a really dark sky.
The other day we took our telescope (8" Dobson - so nothing fancy) to the balcony and were able to see M57, M56 and the comet Garradd - we only have sky view near the zenith. Please note that this happened actually wearing a T-shirt.
When we pack the scope into our car and go to our favourite spot (5 minutes drive) we can see planets and a whole lot of stuff. And this is still far within the conurbation (or "sprawl" - since you're from Seattle ;-). What we cannot see there is the milky way. But even our sprawl and Seattle are of finite size so you can pack your stuff and leave the sprawl for a darker spot every once in a while. This is also a great opportunity for meeting like-minded people: search for star parties in your area.
So, yes. Go buy a telescope. Meet like-minded people and have tons of fun. Take into account that you might want to transport the telescope to get to a spot with better seeing so lifting and setting up are major concerns here. Also buy a decent telescope in order to get more fun out of it and to get a better price when reselling it later should you find that this is not your kind of sport. But in all it is totally possible and worthwhile.