Cristina Hartmann, Lawyer by day, writer by night.
Let's start with skin color. After all, we need to know if any basis exists for interpreting Katniss as a woman of color.
Katniss' skin color.
Collins describes Katniss as having black hair, olive skin and gray eyes. Not very helpful, but let's look at the skin and eye color issue.
Olive skin, according to Wikipedia:
describes a skin color range of some indigenous individuals who are from the Mediterranean and some other parts of Europe, Middle East, and regions of South Asia, Southeast Asia Central Asia and Latin American [sic]. 
So, olive skin encompasses both Causcian and non-Causcian backgrounds. Still not terribly helpful, moving on.
Gray eyes apparently exist, despite my initial skepticism. Gray eyes occur the most often in North and East Europe. There are, however, some instances of gray eyes in North Africa and the Middle East.
Again, very ambiguous. According to her skin, hair, and eye color, Katniss could have European, Middle-Eastern, or North African ancestry.
Other circumstantial evidence of Katniss' heritage.
Katniss lives in District 12, also known as the Appalachia region of West Virginia. If we assume that the ethnic demographics of the futuristic Appalachia reflect District 12 demographics, maybe we can guess at Katniss' racial background.
According to the Census Board, White persons make up 93.9 percent of West Virginia (compared to the national 72.4 percent). So, the odds are pretty overwhelming that Katniss is a white person (of indeterminable origin). Still, she could be in the remaining 4.1 percent! (Note that people of African descent constitute 3 percent of that 4.1 percent.)
If we make the very shaky assumption that District 12's racial demographics mirror modern demographics, the odds weigh heavily on Katniss being of Caucasian origin. Of course, Caucasians can come from North Africa, Middle East and some parts of Asia, as well as Europe.
Is this all much ado about nothing?
Since circumstantial evidence points towards a Caucasian heritage, Jennifer Lawrence's casting doesn't violate the canon's material. As we see in the promotional material, the makeup artists darkened Lawrence's skin a bit. I'd have liked a more yellowish undertone to her skin (befitting the "olive" label), but whatever.
Race seems to play little, if any, role in The Hunger Games. The books focus more on political oppression, tyranny, and television, not race. I wonder if the "layer of meaning" would detract from the core message of the books because of our unfortunate relationship with race.
Sure, it'd be nice to see a minority woman in that role, but I don't think it's a deal-breaker.
Addendum: I should've mentioned that I'm very displeased with the filmakers' decision to limit the casting call to white actresses. To preemptively decide that a racially ambiguous fictional character is white reeks of racism (intentional or unintentional). Perhaps a minority actress could've been a great fit for the role, but we'll never know because that choice was made too early.
: Olive Skin (Wikipedia article) http://en.wikipedia.org/wiki/Olive_skin
 Eye color (Wikipedia article): http://en.wikipedia.org/wiki/Eye_color#Gray
: U.S. Census Bureau: West Virginia: http://quickfacts.census.gov/qfd/states/54000.html
: Caucasian Race (Wikipedia article): http://en.wikipedia.org/wiki/Caucasian_race
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