Eastern Washington doesn’t really get rain like Western WA does, but then you also have to be prepared to deal with real winters. On the plus side, it’s a lot cheaper, and there’s some great horse infrastructure.
The area where I live (Tacoma/JBLM) is a bit of a dead zone for riding. Go further south and it gets better. Go further north it gets better. Vancouver is a great area and there are some really good trainers in the area. Snohomish County also has some great facilities if you’d rather be in the Seattle metro instead of the Portland metro. If you’re into drill or gaming, it’s an absolute paradise no matter where you go.
There are a number of potential pitfalls for building on your own land. You’ll want to take a good look at any parcel for protected wetlands, and some counties make construction very, very difficult.
The nice thing about trails is that so many are open to stock. They’re just not often advertised as such. For example, the whole PCT is open to stock (although I wouldn’t really recommend riding some sections), as well as many of the trails in the National Forests. The Olympics, however, are not that horse-friendly.
As for care, while I’m sure it depends on the horse, the last two I leased were pasture kept year round and didn’t really have any issues. That said, year round pasture can be a bit of a luxury (along with covered arenas actually). Runs are more common, and runs in lower-rent barns get ugly. That’s actually where I’ve seen horses have more problems with hooves in particular. Remember it’s less downpours (despite what the current weather would have you believe…) and more nine months of overcast and spritzing. I would recommend you spend a long weekend here in the dead of winter before you move. The rain might not kill you, but you don’t know how the low winter sun will until you experience it.
PM me if you want more specific information, especially about trails. I’m big into backpacking, so I have a good handle on conditions.