The fact of the matter is that there has not been a significant amount of scientific study as to the effects of having your hair colored during the first trimester, or even during the second or third trimesters, of pregnancy. No one can say, with much confidence that it either is or is not safe to color your hair during the first trimester.
Still there have been a limited amount of studies on animals that have suggested that some of the chemicals that are contained within hair dyes may lead to birth defects. However, in these studies, the animals were exposed to extremely large doses of the chemicals, doses that many times that which a woman would typically be exposed to during the process of having her hair colored. Coloring your hair does not use large amounts of those toxic chemicals. Still, no one knows whether low doses of these chemicals can cause a problem. Furthermore, only very small amounts of the chemicals involved actually are absorbed into the mother’s system.
It is, probably, safe to color your hair during the first trimester. There are alternative products, such as vegetable-based hair dyes, that you might consider if you are worried about exposure to the chemicals in hair dye during the first trimester. Of course, you should check these dyes, as well, to be sure that they do not contain the same types of chemicals that the synthetic hair colors might contain.
Another option may be to consider either frosting, highlighting, or painting your hair. These processes are less likely to put your skin into contact with the chemicals in question. Because the chemicals are absorbed by your body through your skin, such as the skin on your scalp, and not through your hair, these techniques may even further lessen the chance that a potentially unsafe chemical might make its way into your system.
As always, if you are concerned about the safety of a particular product during pregnancy, you should contact your health care provider.