Suppose you had a state slogan on your license plate, and you disliked it. Would it be legal for you to paint over it, or otherwise cover it? (Say, "Ski Utah" or "Water Winter Wonderland," if you objected to advertising, or "Live Free or Die" (New Hampshire) or "Taxation Without Representation" (D.C.), if I disagreed with the political message.) To be clear--you're not covering the license plate number in any way, just the slogan.
Yes, you may cover it up (I don't recommend painting over it though, as you are then altering the plates). This question was definitively decided by the Supreme Court in Wooley v. Maynard (1977). You can find the case here: http://caselaw.findlaw.com/us-supreme-court/430/705.html
This case dealt with an individual who was given several citations for violating the law when he covered up the New Hampshire slogan. He was a devout Jehovah's Witness and the slogan went against his beliefs. In my opinion this case applies to anyone who disagrees with the slogan. Or wish to refrain from saying it.
The Court held:
"The fact that most individuals agree with the thrust of New Hampshire's motto is not the test; most Americans also find the flag salute acceptable. The First Amendment protects the right of individuals to hold a point of view different from the majority and to refuse to foster, in the way New Hampshire commands, an idea they find morally objectionable."
"the State of New Hampshire may not require appellees to display the state motto upon their vehicle license plates"