According to the majority of Islamic scholars, a woman is required to cover everything but her face and her hands. A minority of Islamic scholars hold that a woman is required to cover everything but her eyes. However, nearly all of these scholars permit a woman to uncover her face so that her identity can be verified. There's a link in the original blog entry about Freeman about this.
I personally do not believe that the face veil is obligatory. I wear it out of choice. Even if I did believe it to be obligatory, the school of thought that I follow would permit me to unveil for identification purposes.
Thus, all my photo ID shows my face and I have no problems with being asked to uncover my face so it can be matched against the ID card.
I think that Sultana Freeman is being stupid to want to wear a face veil for a photo ID.
But I also don't think that she should have her license revoked for that reason and be unable to drive. That's what Florida did. I think that Florida should allow Freeman to take a religious exemption and be able to get a non-photo driver's license. This option is available in Illinois and apparently some other states as well, though I haven't found documentation yet on them. The Supreme Court case that I mentioned in the legal issues entry makes it clear that people are permitted to take a religious exemption and get non-photo driver's licenses.
There's something that I don't know if a lot of people understand. It doesn't matter whether Freeman is the only person in the world who holds that religious belief or if every Muslim does so. The Supreme Court is not, and should not, be in the position of determining what the "correct" positions of a religion are. If it did so, it would be involved in "establishing that religion" by entangling the government in how the religion runs itself.
It simply does not matter whether any other Muslim holds Freeman's beliefs. As long as she can present an argument that her beliefs are based in some way on her religion and that she holds them sincerely (which she clearly does), then that is her "religion" even if it is not the view of any other Muslim. Again, the Court is not going to decide which religious beliefs are valid and which ones are not.
Once Freeman has proved that her ideas are based on her personal religious beliefs, then the court looks at whether the government has a compelling interest that justifies infringing on her exercise of her religion. In 1985, the Supreme Court agreed that the state's interest in photo driver's licenses is not compelling enough to override peoples' religions. The Supreme Court therefore said that the state (in that instance, Nebraska) had to allow the woman (in that instance, a Christian who believed photographs were graven images forbidden by her religion) to get a non-photo driver's license.
As far as I know, that is still good law today. If the precedent from 1985 is still good law, then Florida will probably be required to let Freeman have a non-photo driver's license.
Added: Law professor Eugene Volokh comments on this question.