Gila River Conditions in 2nd Half Nov

What would the conditions be in New Mexico along the Gila alternate route up to Pie Town in the 2nd half of November? From what I can gather, this is a transitional period, but I don't know what that means. What are the likely conditions and how bad could it really get? My only experience with the area is being snowed on on the I-40 out of Albuquerque in late December.

Was suppose to hike from the border up to Grants this past spring but had to bail out of the Black Mtn Range (official route) when my lungs felt like they were completely full of congestion and feeling like I was dragging all day. Issue likely goes back a week before I left for the border when I was fighting off coworker's sudden flu epidemic at my office.

Unless a friend is cooperative in helping me get back on in the Blacks where I got off (but I already owe them big for helping me get off), doing the Gila route seems more likely; starting back in Silver City. While I could just wait for next spring, I'm exploring the possibility of going back this fall and wanted to see how realistic is was. My company doesn't like October vacations due to all the customer requests we get prior to fall trade shows, so even early November isn't likey, so I realize I'm pushing the clock a little late.