I have personally never used chains or studded tires and have only used the Blizzak brand of snow tires so I can't comment on other snow tires. The Blizzak tires are truly phenomenal though if you've never used them. My previous car had AWD though so it was exempt in many states when shod with snow tires on all corners but now that I am back to a FWD car then I'll have to keep that in mind again.
Washington travel info (states that some passes will require chains on all vehicles or an AWD vehicle with snow tires, etc. -- good info):
http://www.wsdot.wa.gov/winter
Montana travel info:
http://mdt.mt.gov/travinfo/tire_restrictions.shtml
Idaho travel info: Not inclued because the trip is only about 40 miles through this state and Wisconsin, Minnesota, and North Dakota don't have the mountains that the Western states do. =)
But I'll be sinking some cash for a full set of Blizzaks and most likely a spare set of wheels as they are still quite affordable and a separate set is so much easier.