"Hispanic" is a box on U.S. government forms for immigrants from Latin America, and their children, and grandchildren, to check off.
The category and concept of "Hispanic" doesnt even exist in any other country but the U.S.A.
Its a cultural/ethnic/language grab bag made up to include people from the parts of the New World colonized by the nations of the Iberian Peninsula in Europe (Spain and Portugal). That being the New world south of the Rio Grande and the US Gulf Coast-southward to the tip of South America. Above that line is "Anglo America" (the parts English speaking countries ended up ruling). The Islands of the Caribean - thats a complex subject for a whole nother long post like this).
It means (more or less) the same thing as "Latino", or "Latin American". I would call them "Ibero American".
However there is quibbling: the Phillipines (also colonized by Spain for centuries) are sometimes lumped with Hispanic, and folks from the two mother countries in Europe (Spain and Portugal themselves) are also sometimes lumped in to "Hispanic", and sometimes not. Half of the continent of south america is one country:Brazil which is Portugese speaking. The rest of South America, and all of Central America and Mexico, are in the Spanish speaking world (except there are flyspecks of English speaking in places like Belize and Guyana).
The bottom line: "Hispanic" is not "a race" its a cultural grab bag. Its includes "Whites" ( both pure blood descendants of the original conquistadors from Spain and Portugal, and the millions of European immigrants who flooded into Latin America in the centuries after the Spanish conquests from all over Europe), it includes full blooded red Indians who already lived in the Americas, it includes Blacks from Africa, and it includes any mix of the above. Most folks from Mexico and Peru (for example) are Mestizo (mixed Indian and White). Most folks from the Dominican Republic are Mulatto (mixed White and Black), Argentinians tend to be "Italians who speak Spanish and think that they are British", and folks from Haiti and from northeast Brazil tend to be of pure African descent.
To answer your question:
"White Hispanics" are a "subset" of "Whites" in the same way that White Americas (or White Anglos) are a subset of Whites. They are cultural subdivision of whites,not a racial subdivision. Racially -they are just "Whites" from whatever European extraction they are (just like canadian or America Anglo "Whites").