Is it ok for my Dad to gift his cars to me and my brother when he's no longer allowed to drive?

Rather than complicate things for a future Medicaid application, can you just use the cars and keep them in your Dad's name?
You'll no doubt be driving them to help him get around, so he still is "using" them.
Then, if he does need to apply for Medicaid at some point, the cars will have a lower book value then than they do today and, if you wanted to, you could buy them from him at fair market value and not interfere with Medicaid qualification. Let the depreciation happen while your dad owns them in case you ever have to buy them.
Just make sure your insurance company knows the arrangement so they can properly cover you.

Yes of course he can gift them to you, please don't feel guilty if he can't drive then the car is just going to sit in the drive way but if he decides to sell it to help pay for care then that's a different story.

He can do what he likes with his property; but you'd be well advised to have them valued at the time of transfer and keep records of their agreed cash value. Then if anyone - Medicaid, suspicious family members, whoever - starts asking questions in the future you'll be able to supply reliable information. Ask someone respectable to do it: a reputable sales network, a motoring organisation or something like that.

Sunny5,
Ask an attorney. If you care for him and use car for his care it may not count against him later. We were told by lawyer we could claim up to 50% of OUR bills for taking care of Mom. Heat, electric, insurance for home and auto, cable and payment on one of our cars. OR we could seek retractive caregivers pay. We are doing neither but it's nice our lawyer gave us options.

It's not OK to gift anything if he is on Medicaid or if he will need Medicaid within the next five years. However, he can sell the car at fair market value, put the money in the bank and use it for his care. Medicaid will allow that.