You can have it, and you should just enjoy it and not worry about the type of wine. It's not like you are having a sugary beverage like Baileys or Frangelico. In moderation, of course. I have it on weekends unless there is a special occasion during the week.
A glass of wine is allowed on Phase 2. Make sure you are getting real wine though and not one of the "wine beverages" that hang out in the wine section now (like Arbor Mist). Those are loaded with high fructose corn syrup and are a definite no.
I think Dr. A encourages red wine for the health benefits. Personally I prefer chilled white in the summer and red in the winter. As with all things be aware of servings and exercise moderation. Too much wine can lead to too much unplanned eating. (we won't even talk about the headache part!)