This is a pretty straightforward winter ride that can be done inside of two hours by a determined rider or group of riders. Describing the exact route is a little tricky, but you get the idea by looking at the map and reading this description.
Start at Ivory Jack's. There are two ways to head out from Ivory Jack's. Either way puts you in the same place. The first way takes off down the commuter trail alongside the airstrip. You come out by the railroad tracks at Sheep Creek. Follow the bike path over a little bit from the railroad crossing (about 200-300 feet or so) and turn off the bike path onto a snowmachine trail heading off across the valley. The trail (sort of) contours alongside the base of the ridge north of Sheep Creek. After a few miles, you come out right at the bottom of the hill where Ballaine starts up the hill. Ride the bike path over across the bridge until you get to a major trail crossing. You will see a sign on a tree on the south (left) side of Ballaine telling you that this trail is on private property and is only for winter use, not that it's possible to ride it in the summer, mind you! Cross Ballaine Road here and head off out toward Fox on the main trail.
The other way to start off this ride is to go down the road behind Ivory Jack's that starts off aiming for where Ballaine Road starts coming downhill. After a bit, this road ends at a trail going off to the left. Follow it for a bit across O'Connor Creek (watch out for the overflow) and then turn right at the road (Dawn Lane, I think). Turn left at Harper's Road, then left at Miller Hill Extension. At the first major trail going off to the right, you turn and follow this trail across the valley to Ballaine to the trail crossing mentioned in the above paragraph.
Anyway, when you cross Ballaine, the trail immediately goes perpendicular to Ballaine, then makes a sharp right turn and crosses over Goldstream Creek at a bridge. Follow it to the "Five Trails" intersection and pick up the main trail going alongside the base of the ridge. There are several satellite trails and side trails I will leave you to explore (one goes up higher alongside the ridge and eventually crosses an old railroad bridge, this trail is the old Tanana Valley Railroad grade).
Follow this main trail out toward Fox for a few miles. The last part of it will get a little ragged and munged up (depending on when the last time the snow machines packed it down). You will come to a turnaround right before the mine. Pick up a trail a little to the north of the one you came in on and follow that back to the intersection with Ballaine. Take either route back to Ivory Jack's. Total distance is around 18 or 19 miles and is doable in under two hours, if you push it.