Application for registration shall be made to the county treasurer in such form as the director prescribes and shall state the name and address of the applicant, state a description of the snowmobile, including color, manufacturer, and identification number, and be signed by at least one owner. Application forms shall be made available through the county treasurer's office of each county in this state. Upon receipt of the application and the appropriate fee as provided in section 60-3,210, the snowmobile shall be registered by the county treasurer and a validation decal shall be provided which shall be affixed to the upper half of the snowmobile in such manner as the director prescribes. Snowmobiles owned by a dealer and operated for demonstration or testing purposes shall be exempt from affixing validation decals to the snowmobile but are required to carry a valid validation decal with the snowmobile at all times. Application for registration shall be made within fifteen days after the date of purchase.