Can you knockout a gene specifically in the dorsal root ganglion in adult mammals?
It requires two genetic constructs to create a conditional KO organism. One parent with a transgene that expresses a DNA recombinase (such as Cre) after the promoter of a gene that is ONLY expressed in your tissue of interest. The other parent contains a modified gene of interest to be removed in the presence of said DNA recombinase but is fully functional otherwise.

Therefore, the ability to target a Knockout to a specific tissue is dependent on identifying a gene that is only expressed in the tissue of interest.

It is actually easier to create a whole animal KO, but because gene products can have different functions temporally in development and in different tissues, a whole animal KO may be lethal, whereas removing it in a specific tissue may not be and allows study of the effects of said removal.

Thus, if your gene of interest were lethal when removed from whole organism, AND you know of a gene that is only expressed in the DRG, you would have incentive to see if a CKO animal could be made.

A brief search on Cre Lox technology will bring up 1000's of images and articles.
Here is one and a nice illustration: