The main rule is, YES, you may travel with guns and ammunition for hunting and sports, but only in checked-in baggage and under certain strict conditions.
Guns and ammunition
Gun license and all other official documentation required by the destination country must be provided at check-in.
Passengers are solely responsible for any fines or other expenses that may arise if this is insufficient.
Guns must be unloaded and in an unusable condition while they are on board our planes.
If traveling with ammunition, it must be transported in a suitable container which protects it from knocks and crushing, such as a wooden, metal or a hard plastic case. The case must be marked with the name of the owner and a description of its contents. The maximum amount of ammunition allowed is 5 kg (11 lbs).
Guns and ammunition may only be carried in the baggage hold.
If the above conditions are not fully met, WOW air reserves the right to refuse to transport guns and ammunition.
It is also permitted to travel with weapons considered antiques or heritage items: guns, swords, knives, etc; but only in checked-in baggage and under certain strict conditions.
Passengers traveling with guns and ammunition to airports in the United Kingdom must note that they should proceed to the Red Customs Channel where, in the presence of a Customs Officer, their item(s) will be returned to them. Guests will be required to provide evidence of ownership and may be asked questions. WOW air is not permitted to return guns and ammunition via the normal baggage reclaim belts.
As a preventive measure against spreading infectious diseases of freshwater fishes to Iceland from other countries, it is prohibited by law to use fishing equipment, including waders and rubber boots, which have been used abroad, unless it has been disinfected according to valid rules. A certificate of disinfection issued by an authorized foreign veterinary officer will be accepted if presented on entering Iceland. If a certificate cannot be obtained, the fishing equipment must be handed to customs officers upon entering the country for immediate disinfection at the owner's expense.