S.W.
All preschools start in fall. There are no schools that would start in the winter or spring. That being said, you may find a spot at a preschool in the winter or spring but your child would be way behind in the fact that they would know no one and everyone else would have had all year to be friends. Also, you may find a preschool that has a summer program, but those are more like day camp then preschool.
My son is a may baby and you just start them up in preschool in fall. Starting them earlier just isn't really done, they really aren't ready for preschool much earlier than that. There are a few preschools who have programs for 2.5 yr olds. Also, I wouldn't suggest starting a may baby early in school, they just are behind emotionally since there are a ton of fall babies that will be in school with your may baby. I have that problem with my son in kindergarten. He is only 5 and there are a lot of the students that are 6 already and he is behind emotionally than a lot of them, especially way behind the girls.
All that being said... There is a preschool in Woodinville and one in Kenmore that has a 2.5 year old class you may want to see if they have any space. It is Morning Star Preschool http://morningstarschool.com/
But for a general rule... for preschool for a 2.5 yr old, they need to be 2.5 by Sept 1st or for three year old preschool, they need to be 3 by Sept 1st etc etc. Hope that helps! And by the way, I highly suggest Morning Star, it is a fabulous preschool! :)