That I am not sure about. However, I can tell you this. I grew up in Vietnam. I was very very dark. After living here for 3 years, I went back there to visit people and I was snow white compared to everybody else. That should tell you something about people's ability to adapt.
Thats why you can be fairly light skinned, and then after living in a place like Arabia, eventually your family genes will change and the generations will become much darker skinned, or you can just get a tan! Haha, but thats basically Skin Color in a nutshell.
I'm going to have to nitpick this one. Aside from some kind of mutation or interbreeding with the natives of Arabia, your "family genes" will not change. Your descendants may have more skin pigmentation, but that has nothing to do with genetics. Enviromental pressure (in this case, the almost constant exposure to the sunlight) makes the people adapt, on the individual basis, to live in such environment.
In other words, if you and your descendents abstain from interbreeding with the native Arabians for 10 generations and then that generation decides to go back to North Asia, their skin color will eventually become light again.