What could cost my teeth to feel sensitive the morning after drinking wine?

Dehydration.: Drinking alcohol can lead to dehydration which can lead to tooth sensitivity. Also some report drinking alcohol can increase the likelihood of grinding your teeth, which could contribute as well.

Wine is acidic.: Wine is acidic. If you have exposed roots from recession or wear on the biting surfaces of the teeth there is exposed dentin. The acids open up the tubules of the dentin which opens a direct channel to the nerve of the tooth. Once the tubules close back up, the sensitivity goes away. Sensitivity toothpastes or a stannous Fluoride gel used daily will help.