A first activation of Eureka Peak on snowshoes turned out to be quite a workout. The basic climb description is about 2.5 miles one way and 1200 feet of gain, but the real work is off the trail with the last half mile being particularly steep. Since there is no trail to the top this would be difficult to do without snow cover. And the steep sections might be unsafe later in the spring on firm consolidated snow without crampons and ice axe. 

On Highway 26, head to the Trillium Lake SnoPark, 1.5 miles east of Timberline Road. This SnoPark can get pretty crowded on nice winter weekends, so you might want to arrive early. (Oregon SnoPark Pass required). Head down the hill 0.5 miles and go right on Perry Vickers Road. Go another 0.5 mile and turn right onto Chimney Rock Drive. Note that this is essentially the route around Trillium Lake and you'll have the company of many cross-country skiers and snowshoers. 
After about 0.5 miles on Chimney Rock you'll veer off the main route onto Sherar Burn Road. If there isn't too much snow you'll may see a sign on the left with no writing - this is where we decided to start our way through the woods towards the summit. With several feet of snow on the ground you are above all the brush, branches and downed trees in any forest and able to head up the ridgeline to the summit, about 0.8 miles on. However, note that it gets increasingly steep and more heavily treed as you go, with some slopes up to about 45 degrees. 

We had nice weather with broken clouds and touches of sunshine, but it was cold at the top, we were tired after three hours on the trail, and we elected to each get four quick contacts from the folks waiting for us on 2m FM and head back down.  

This summit is pretty challenging and you may find nearby Mud Creek Ridge a much more approachable snowshoe activation. 

Note that the Eureka Peak Trail doesn't go near the summit Eureka Peak - it's even hidden behind the legend of this map https://www.fs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb5359515.pdf.
 
Here's the experience of another snowshoe party that summited Eureka Peak several years earlier http://loomisadventures.com/blog/climbing-eureka-peak-oregon-winter.