Oysterhead,
On our 3 day weekends climbing the highpeaks, Mt. Jo was one of our routine "Just after we get there" or just before we leave" favorite hikes.
For winter, You will find it completely broken out probably anytime after 9AM on a weekend morning. Perhaps later on most weekdays.
You'll also see a lot of families up there, less inthe winter, but still a lot of folks do this peak. It is an excellent first winter peak.
After you leave either the trail by the parking attendant booth or the Loj building (Note, Not the Hiker and Campers Building, and it is in the opposite direction as the trail to Marcy Dam), you will wind around Heart Lake for a couple of minutes. You have a choice of 2 trails:
The first right you come to is the short, steeper trail. This isn't bad in the winter, but you can get some icy sections sometimes if there is a thaw.
If you continue on at that intersection, you will come to the longer trail in a few minutes. This trail is less steep and just winds around the mountain a bit more.
I cannot recall a trip taking more than 45 minutes (45 minutes was when I had my 2-year old on my back) up and likewise back down. I don't think total elevation gain is much more than 750-800 feet.
Good luck and enjoy the views.
