I am assuming, for example, that well-to-do, Spanish-looking Cubans like Desi Arnaz would have been considered white for all intents and purposes.
What about mestizo-appearing Mexicans or Mexican-Americans? Do we have any documentation regarding how they were treated, and how they would have fit into the South's system of racial segregation, which seems to have been based on a white-black binary without much consideration for the gray area that might be represented by a Mexican of mixed Spanish and indigenous Mexican ancestry?
EDIT: Spelling fixed and post expanded for clarity.
My background is in CA education. In the Southwest there were separate schools for Latinos, and though they were not backed by the law, they were common. The claim was that the separate schools would teach Americanization. In the 1931 Lemon Grove Incident in San Diego families of 75 Mex students challenged the school board for segregating the children to a "barn school" and argued that most of the children were American born and spoke English. The judge sided with the Mx families as CA law did not authorize separate schools for students with Mexucan parents. (It did for Indian and Asian students though; San Francisco had a school called The Oriental School to segregate Chinese students and later Japanese.)
http://www.sandiegohistory.org/journal/1986/april/lemongrove/
Eight years before the Brown vs Board ruling, in Mendez vs Westminster (CA) the judge decided the separate education of the Latino children was not equal in quality. Sylvia Mendez had been turned away from the "white school" while her lighter skinned half Mexican cousins with a French last name were allowed to attend. The judge ruled that segregating schools for Latinos "suggests inferiority among them where none exists."
Then the Governor Warren of CA repealed the law that allowed segregation of Asians and Native American students. Later Warren went on to become the chief justice of the U.S. and wrote the Supreme Court decision in Brown v. Board.
Salvatierra v. Independent School District was Texas' first segregation case but I'm not too familiar with that one.