Park at the very popular Meadow Mountain
trailhead just north of Minturn and find the start of the trail at the SW corner. It can be a zoo on weekends: expect dogs, snowmobiles, tubers, racers in training, snowshoers, etc.
Climb up rolling terrain, following any path you choose. You can follow the summer road (Line Shack trail) to keep the angle very low, or just charge straight up, which is very rolling. There is a large flat section about a half mile up, but otherwise it's a nice climb all the way to the top.
This route ends at the top of the best ski line in the area, but you can keep climbing for another 400 vertical feet (about a mile) and get to an old cabin (the "line shack") that has a wood stove and shelter from bad weather.