While State laws may vary how they view the question for state taxes, there is only one IRS who collects federal taxes, and they state clearly (here:
http://www.irs.gov/pub/irs-pdf/p463.pdf (page 15)):
Advertising display on car. Putting display materials that advertises you business on your car does not change the use of your car from personal use to business use. If you use this car for commuting or other personal uses, you still cannot deduct your expenses for those uses.
PS: it doesn't matter how many vehicles you have, it you drive to visit grandma in it or go to buy groceries, it is personal use. If you use it to conduct work, it is business use. The IRS frowns upon claims to the contrary.