There was a major campaign fought to recover Kiska and Attu (taken by the Japanese at the same time as the Battle of Midway, June, 1942) with some thought of moving on to take the Kuriles chain (owned by Japan at the time, now held by Russia) and threatening Japan from the North. There were periodic bombing raids on Paramushiro in the Kuriles (one of Japan's largest naval bases, the Pearl Harbor attack force had sortied from it) right up to the end of the war.
Flying conditions were miserable most of the year and, after Attu and Kiska were recaptured, the theatre was stripped of much of it's men and material.
In a fine case of not learning lessons, the AAF B-29 squadron my old man was in was sent to Alaska right after Dad mustered out (late 1945) and, as Dad put it, most of his friends died flying into moutains in the snow & fog over the next few years. Yeah, Dad was bitter about that.
Hank