In the grand scheme of things, not very at all. The Japanese wanted the Aleutians under their control to prevent their use as bases for air attacks on the Home Islands. It doesn't appear that they checked the weather... the Aleutians are some of the most inhospitable places on the face of the Earth for piston-powered aircraft.

In fact, arguably the most important thing that came out of the Aleutian campaign was that the US managed to capture a nearly intact A6M2 "Zero" fighter. There had been three others captured prior to this, but they had all been seriously damaged (one was actually frankensteined together from pieces from multiple planes). While "Koga's Zero" did not, in fact, influence the creation of the F6F Hellcat as is often claimed (the first Hellcat flew months before the plane's recovery), testing DID find the limits and weaknesses of the Zero and how best to exploit them.

To the approximately 6000 men killed during the campaign and their families, though, it was the most important thing ever.