This year and last the Cog railway has stayed open in winter. The train stops before treeline, so it's the best of both worlds: plowed road but not too much noise & smoke.
Use the original trailhead - park all the way up at the end of the road (by the second station), cross the tracks and look for a footbridge to the right of the water tower.
Foot traffic is pretty light, so bring snowshoes and give yourself ample time to find & break trail. Axe not needed unless you get lost and wander into a ravine.