The laws governing the legal use, storage and carrying of firearms are constantly changing. Below are the applicable laws in the State of South Dakota  as of 4/23/2013. The below information is designed to be a guide and not the final word. If you have specific questions, please refer to the State of South Dakota legislation at legis.state.sd.us. Another great resource is the South Dakota Secretary of State.

22-14-10. Lawful uses of unloaded pistols or revolvers--Concealment--Exempt from permit requirement.
The provisions of § 22-14-9 do not apply to any person carrying any unloaded pistol or revolver for the purpose of, or in connection with, any lawful use, if the unloaded pistol or revolver is carried:

(1) In the trunk or other closed compartment of a vehicle; or

(2) In a closed container which is too large to be effectively concealed on the person or within the person's clothing. The container may be carried in a vehicle or in any other manner.

No person who complies with this section may be required to obtain a permit for the lawful uses described in this section.

NOTE: The South Dakota Attorney General released a statement with regards to carry firearms in a vehicle. The Attorney General's explanation.

§ 32-20-6.6. Carrying firearm on motorcycle or off-road vehicle-Exception for holder of concealed pistol permit or disabled hunter permit-Enforcement-Violation as misdemeanor.
No person, other than a law enforcement officer or conservation officer, or any person on the person's own land or land leased by the person, may operate or ride on any motorcycle or off-road vehicle with any firearm in the person's possession unless the firearm is completely unloaded and within a carrying case which encloses the entire firearm. However, this section does not apply to any person who is carrying a pistol and possesses a permit to carry a concealed pistol issued pursuant to chapter 23-7. This section does not apply to any person who holds a permit issued pursuant to § 41-8-37 while engaged in hunting from an off-road vehicle in accordance with the provisions of the permit. This section shall be enforced by all law enforcement officers including conservation officers. A violation of this section is a Class 2 misdemeanor.

§ 32-20A-11. Restrictions on carrying of firearms-Violation as misdemeanor.
No person other than a law enforcement officer or conservation officer may operate or ride in any snowmobile with any firearm in his possession unless the firearm is completely unloaded and within a carrying case which encloses the entire firearm. A violation of this section is a Class 2 misdemeanor