I realize I'm super late to the party since this post is almost two years old, but I'll respond anyway for others who may venture out there. Right at the Wedge overlook (where you will probably park) there is lots of cliff exposure where you could fall off if you are being stupid. The actual trail has only one or two spots that I recall being even remotely sketchy in regard to being near the edge. They were both in the first mile or so. There are only a couple spots that would probably not see enough sun to get icy. Most of the trail should see good sun exposure. I rode it in late March and again in June, though, so a mid winter ride could have snow, but again its not really near the edge.
I took a half dozen 12-13 year old scouts (several of which were very new riders) out on Goodwater and all of them survived. They complained a lot, but they made it. I don't even think we had any crashes, just a couple tip overs where someone didn't get a foot down fast enough. It is a good trail for new riders-- not very technical-- I never even dropped my seat. Fairly minimal elevation change, just lots of little ups and downs as you ride through the washes that feed into the canyon. It is a fairly long ride. 22 miles if you do the whole loop. The last five or six are on double track and go very quickly till the last hill back to the up to the overlook. The scenery is great if you like the desert.
We did this trail on the way to Moab and drove on dirt from Highway 10 to the overlook and then all the way over to Highway 191 just north of the interstate. The road to the Wedge overlook is well maintained and is fast driving. The drive from the Wedge to 191 gets considerably rougher the closer you get the the highway. There are some cool canyons that the road winds through. It would have been bad if we can encountered traffic in the narrow canyons since we were pulling trailers, but it was a good drive.