The short answer: American Indians who are fullblood aren't often able to grow enough facial hair to have a good mustache or beard.

My ex is Puerto Rican, a mix of Indian (Taino) and Spanish. He had a beard and mustache for years, but they were on the thin side. In general American Indian men didn't (historically) wear beards in images recorded by early non-Indians. As to whether they could grow them, that's another matter. My ex told me that Indian men usually couldn't grow beards, hence the thin nature of what he could grow as a mixedblood.

Mixedblood and blood quantum are highly charged issues in the Pan Indian community. Indians and African Americans commingled just as Indians and Euroamericans commingled. The blended genes certainly contributed to a variety of physical possibilities, like growing beards or baldness. (It maybe a tradeoff: no beards but hair on top--you don't hear much about baldness in American Indians. Here is a link (not one I know anything about, but it doesn't look completely crackpot) The dominant features that are commonly recognizable tend to mean that the darker features showed up when one parent was white and the other Indian, so a child was recognizable as Indian, but were less likely to show up when one parent was African American and the other Indian. I have spoken to African American students at my university who are interested in tracing their family records because they know of an Indian heritage in the family. It was as if the Indian heritage vanished or was buried, especially in the days when "one drop of Negro blood" (particularly in the South) meant that you were considered ALL African American. Ah, racism and absurd race laws.

SRS