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.
Hope this is helpful.
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.
I climbed Mt Massive in July, 2017. I started at 3AM, so finding parking wasn't an issue. But if you get there later in the day, you might have a problem finding close parking. The trail is well-defined. The first part of the hike is fairly long--it leads you through a forest for several miles. This part of the trail is almost flat, with minor elevation gain and loss. Eventually you reach a fork in the trail and start climbing. You'll eventually pop out into a wide expanse of hill. The trail is partially paved with stones. The mountain still had a considerable amount of snow on it, but the trail was clear. Some parts of it were soggy but not enough to slow you down. You'll reach a saddle where the trail branches. From here, you will have to do some scrambling over large boulders to the summit. On some parts, you can choose between more or less difficult routes. I wasn't able to find a registry on the summit. There are fantastic views in every direction--especially to the east. It took about four hours to summit. I only spent a few minutes on the top and headed back. About an hour later, clouds descended on the mountain and it rained/snowed a little, then cleared up. Overall, an excellent and not too strenuous hike.