Is Rainbow Dash an alcoholic?

If the cider is hard then yes if it isn't then no.
To put it like this: When cider starts to “turn” it begins to become carbonated as fermentation turns it into alcohol. As cider becomes exposed to oxygen, airborne yeast mixes with the cider's natural sugars to produce acid. With this process, apple cider becomes alcoholic and eventually similar to vinegar.
To tell the cider is hard the colors are golden-beige then it's alcoholic.
Simply put, the difference between apple cider and hard cider is the alcohol content (or the lack thereof).

There are points to support both arguments.

On one hoof, it does not go through the fermentation process.

On the other hoof, it is foaming, as only alcoholic cider does, and there are no fillies or colts in the line.