Yes, but it is White Oak accents … not Red Oak! And, it is generally "burned Oak", they char the inside of the barrel. (Or a mix of burned or not, or a mix of 1st year burned, 2 nd year burned, 3 year burned to get the desired flavor). They may also use a mix of French Oak … it is a big deal thing in wine country!
The length of time they age it, and what it is aged in all make a difference. I used to have a client who had his own wine label, and they pay the wine makers a lot for their knowledge!