You'll have to register the trailer and ski in Washington, here's a link on what the cost is most likely going to be:
http://www.boat-ed.com/wa/handbook/index.htm (scroll down to table of contents and click on link, you'll find a section on registration fees and reqs. )

Or here's the direct link:
http://www.boat-ed.com/wa/handbook/toc.htm
The fees:
http://www.boat-ed.com/wa/handbook/register.htm#fees

I insure through progressive, they're the cheapest I've found, but they only sale year long policies. I just cancell it whenever I'm done riding for the year and they refund the unused months. Might seem like a PITA, but it's not too bad, a couple of minutes on the phone is all it takes to renew or cancel my policy, and I never had a problem with them.