as has been mentioned, vikings did use basically longbows, but a simplified version to what is often pictured. at the same time, things like the holmegaard would have been in their lineage, and it is possible that there were some remnants of creative bowyery still alive. finally, the lapplanders made up lots of nomadic tribes that would wander the arctic circle, and it is possible that they did not used the longbow style. a common argument for longbows is given in that they are easily constructed and standardized-good for arming a fighting force. tribes, families, artisans, etc would not have had that stipulation. at the same time, the wood options there were somewhat limited to things like elm, yew, and birch type trees.
viking "empires" at different times included bits of north america, africa, asia, europe-they have found period danish money in trade by the people of the sahara. the vikings would have, as mentioned, used many bows of different types. those found now that we can attribute to having characteristic norse designs will likely be almost all longbows-but that doesnt mean when pillaging pocketbooks and women they would have turned down fine shooting weapons. SOM
