I'm posting a trip report in case anyone (like me) is looking for a quality hike that can be done with kids. My daughters are 7 and 9 and got new snowshoes for Christmas. This was a great hike for them (and us).
Getting there: The directions on the main Chief Mtn page on this site are good, so I'm not going to repeat them. When you park, you'll be looking down at the top of the chairlift for the soon-to-be-opened Squaw Pass ski area. Also, when you get off I-70 at Evergreen Pkwy, Squaw Pass road (103) is a right turn, not a left, as is stated on the main page. That'll be obvious to anyone with a map, but I thought I'd mention it.
The Hike: Again, what's already posted here is good. At this time of year, with virtually no snow in Evergreen, there is 6-18" on the trail, and it made for easy snowshoeing. You can walk it as well, as the snow is packed, but you will sink through in parts, and it messes up the trail a bit. The snow disappears around treeline. Temperatures run about 15 degrees colder than in Evergreen. Of course there is the wind; brutal at times, but there is some shelter behind the rocks at the summit.
People generally refer to this as a short, steep hike. Even with 2 kids, this did not seem steep. It's a steady even climb, but not too strenuous. Also, distances have been given as 1 or 1.5 miles (one way), but the sign posted where the trail crosses Old Squaw Pass road says it's 2 miles. After walking it, I'd say it's definitely more than a mile, probably closer to 2.
On a nice winter weekend day, we met about a dozen people on the trail. There was enough traffic to make following the trail easy. If you're not adventurous, don't try this right after a sizeable snow; the trail would be difficult to follow.
Conclusion: Breathtaking views, pretty easy climb. A great way to introduce yourselves (and your kids) to winter hiking.