I don't think I can directly link, but what you want is American Community Survey Table S1810 with New Mexico County Geography.
Start here:
http://factfinder2.census.gov/faces/nav/jsf/pages/searchresults.xhtml?refresh=t
Enter S1810 for your search topic. This should give you four tables named Disability Characteristics.
From the options on the left, now select "Geographies".
- For geographic type, select County.
- State, select New Mexico.
- Lastly select "All Counties within New Mexico" and then click "Add to Your Selections".
- In the top right corner of the Select Geographies
popup, choose Close.
Now, pick the table of the four choices that you prefer. I would suggest 2010 ACS 3-year estimates, as it has data for the most counties. This will give you your table of results.
Click Download and use the default choice. This will give you a CSV file that you can use to create a dbf which you can join to county geometry to make your map. The CSV file is going to need considerable formatting before you can use it as a DBF.
Note that even with the 3-year estimates, there are only estimates for 20 of the 33 counties in New Mexico. In order to get estimated total population with a hearing disability, you need to add up these four columns:
VC04 HC02 EST
VC08 HC02 EST
VC015 HC02 EST
VC023 HC02 EST