I have been over both routes from Chama to Osier. Here's my .02.
The Forest Service road from Hwy 17 is 17 miles long, gravel and in dry weather OK for a regular vehicle. I just drove it 2 Fridays ago after an overnight snowfall and it was quite "greasy", it was not a fun drive even in a four wheel drive pickup.
The southern route from Apache Canyon is an adventure even in dry conditions. I have driven it in a 4 Runner and the most difficult part was fording the Los Pinos. In dry conditions that was the only place I needed 4 wheel drive. I have also been over that route on a snowmobile and that was A LOT more fun!
Someone mention that the road to Sublette was off of the north access to Osier. It is BUT that road is not marked and the last 1/4 mile is a steep downhill and very rocky.
For what it's worth,
Rich