Correct me if I'm wrong, as it's been a while since I drove the whole Dome road FS289. But I remember the top section being quite easy until it starts dropping off the mesa. I would think a passenger car coming from Los Alamos would be okay, though one would probably have to walk a ways from the Dome road FS289 to the true trailheads. The lower section is quite a bit rougher, but not crazy; I have driven it in a Subaru without issue.
FS289 is a bit rough at the south end but yes a Subaru or equivalent could probably do the whole thing. The north end of the road is in excellent shape and can be driven by anything.
The Dome Road however is a different story. It was really rutted from people driving through when it was muddy and now it has hardened up. 4WD is not needed but some clearance is necessary.
Whoops, sorry, I was referring to FS289 as the Dome Road. I stand clarified.
As a Subaru owner, I always appreciate a little more detail about the middle ground between "passenger" and "4WD."
When talking about driving back roads I determine if my vehicle can do it based on 2 factors: 4WD and clearance. Too often I think people say 4WD when the mean clearance. To be clear no roads that I have driven in this area require 4WD although having the higher clearance of an SUV or truck is helpful or even necessary in some place (i.e. the Dome Rd). Carefully driven *most* passenger cars could do all of FS289.
Also, I have seen one map label the southern portion of FS289 as the "Dome" road. However, when I say Dome Road I am referring to the Saint Peter's Dome Road that is a turn-off from FS289.
Hope this is helpful, I'll edit the Dome Wilderness page to be clearer for people trying to access this area.