I looked at my Topo! software and it appears that access to Garfield will still be possible year-round. Or, more specifically, between Nov. 1 and April 15, it looks like one would have to hike the road about 2.5 extra miles (5.0 miles round-trip) and ~100 feet of extra elevation gain from where they've gated it at Road 5640 (Taylor River Road junction?). This would require an extra two hours round-trip and could be done in the dark if necessary.
While I haven't been up the road past Garfield from Nov. 1 to April 15, I have been up it in June. In June it was extremely water-logged (lots of fording). I imagine it would be even worse (deeper) in the winter, so you might have to hike the road to Garfield anyway unless you had one of those huge Broncos.
Access to the north side of Garfield via Taylor River road will not be affected, presumably.