The 1885 New Mexico Territorial Census in now online for free at FamilySearch.org. This is not only the indexes, but the images of the actual census! Previously, you could only find these records on microfilm or on Ancestry.com.
Here is the link to the 1885 Census.
The 1885 Census is important because most of the 1890 U.S. Census was destroyed. There is no other U.S. Census record between 1880 and 1900 other than the 1890 Civil War Veterans and Widow's Census.
A blank form that you can use to transcribe the 1885 New Mexico census can be found at this link.