It depends on several factors, down to cultural, socioeconomic, biological, etc…
Living in an Anglo/ European dominant country (U.S., UK, Germany, etc.), what do you see in print, pop media?
That's right. White, blonde, blue eyed males and females. Who dominates cinema and television roles? White men.
The Anglo/Euro culture is saturated in white supremacist propaganda. Mind you, I'm not necessarily talking bout Ku Klux Klan, skinhead, Nazism, and the like… but white culture will do what any other dominant culture will do: assume they are the best. There is always an ethnocentric bias in whatever country you live. Even if you live in a diverse, multicultural neighborhood or town, overall, especially in the U.S., Caucasians make up the largest population. There is no reason for marketers, media outlets, advertisers and the like to focus 90% or more of their energies and focus on anything other than the target demographic, predominantly white people.
If you go to Asia, (whether south asia, southeast asia, northern asia) you'll see not one Anglo face on the billboards. Of course they're going to represent the faces and people that the masses are going to relate to. They're going to use faces and people that the largest population is going to want to see.
The problem is, if you are a minority (Black, Latino/Chicano, South East Asian, South Asian, etc.) you're already at a disadvantage. That's not to say that if you are a minority, that you cannot date women outside your group. However, because of cultural stigma and other factors, it can cause women who have been inundated with media images to view white men as the ideal man; what else can these women do, when they've been bombarded with stereotypical images of white men as heroes, the main protagonists of stories, high sex appeal, etc… On a rational level, they will view white men as more ideal, and even superior.
On a biological level though, we see that this is not the case. People might be apt to brainwashing on a cognitive level, but biologically, women are still attracted to strong, masculine, dominant men. Whether that man be a Black American with slave ancestry, or an African native, or an Mexican with indigenous blood, or a South Korean, or Sri Lankan,… it does not matter. If that man is truly attractive in a holistic sense, then that man has just as much sexual opportunity as the white man.
You will see, however, that most girls (white girls, but also Asian and Latino) in the U.S., will idealize and fawn over white male actors/ models/ singers because… that is what they've been trained to do from watching TV and movies, books and stories written from an Anglo-European bias. They will have little or no problems dating white men. Because socially, it is accepted. White men are considered the "standard", while everyone else is a notch or two below…
So yes, absolutely, if you're not a white male living in the U.S. or most parts of Europe, you are at a disadvantage. But it doesn't mean you have no shot… There are so many different reasons and variables at play, but I just wanted to touch on a little bit here. A lot of this is sociological/ historically based…
One interesting story though, just food for thought: In the early 1900s, during a period of large waves of immigration, particularly Asian immigrants, the influx of Asian people spurred government legislation that banned miscegenation. That is, there was government law, part of the Constitution… that prohibited white women from marrying outside of their race. This was largely in response to not only black Americans, but primarily as a result of "Yellow Peril", and to put it in a nutshell, white men were afraid that the "yellow" people were going to steal their white women away… a similar phenomena that arose during the 1800s onwards, where black Americans were stereotyped as brutes who were going to steal and rape America's white virgins…
In short, Hell Yes… white men have it easier. in America. Or Europe. To say otherwise is to be color blind and ignorant of reality. But it doesn't give men of color any excuses not to pursue women outside of their group. Come to Asia, come to Central, South America, though… you might be deemed exotic, if you're white… but that exoticism is a small, small, boost compared to the ethnocentric, social biases you'll face if you step outside your home country.
I would never use race as an excuse. Because even if a girl on the outside, overtly states that she only goes for "X" group of men when dating… it doesn't matter. Because that might be true… but that's more a result of not being exposed to sexy, attractive men from that group… it only takes 1 casanova from an outside group to break in and tear down her preconceptions of dating outside her group.