there are lot of ski slopes in the Tohoku region I havent tried any of it yet but a friend who have skied the area recommends APPI. A lot of the ski trip we go to we sign up with the outdoor recreation on base and they take care of the driving and some of the gear.
if you want to go on a refreshing hike I recommend you go Oirase gorge and hike the 10km trail towards lake Towada. Along the trail you will see numerous falls to go along the very dense wooded area.
Equipment: comfortable shoes, water and camera