"Snowmobile" means a self-propelled vehicle that is capable of traveling over snow or ice that (1) utilizes as its means of propulsion an endless belt tread or cleats, or any combination of these or other similar means of contact with the surface upon which it is operated, (2) is steered wholly or in part by skis or sled type runners, and (3) is not otherwise registered as, or subject to, the motor vehicle excise tax in the state of Washington.