Winter and spring ascents are done occasionally, especially by ski mountaineers. The normal route is the west face via the Halfmoon Creek Trailhead.
It seems like the west face of Massive is actually very seldom visited in winter due to the long distance to get there in winter. The east face route is actually the normal route in winter, and can be approached from more than one direction.
One route is from the Fish Hatchery, and in winter, this may be the most used route. Another route is to follow the closed road from the closure to the summer trailhead and climb the standard Colorado Main Range Trail. The shortest option seems to be the route up Willow Creek.
In the "getting there" portion you say that the closest airport is Denver International. I feel its worth mentioning here and in the Mt. elbert description mentioning Leadville Municipal Airport which is the highest public airport in the US at 9927ft. Although you cannot "buy" a ticket to get there, my dad an i fly into there all the time. So for those who want to climb in the area and have access to a private or charter plane, leadville airport is a way better place to fly into.