Is it true that drinking alcohol will hurt your singing voice over time?

Alcohol is a dessicant: it replaces water in your body and dehydrates you. Note that this is why you urinate so much when you drink alcohol. Also not that that you urinate clear, a normal indication that your body is well hydrated. In actuality, this is happening because that alcohol is forcing the water out of your body.

Anything that dehydrates you is, in an objective sense, bad for your voice, as the mucous membrane tissues which make up your vocal mechanism are approximately 90% water. The protective layer of mucous they secrete is nearly 100% water. So, if these delicate tissues become dehydrated, they stop secreting mucous, and are more subject to stress and injury. Some voice teachers will advice avoiding alcohol completely because of this. However, alcohol in moderation, accompanied by enough water to maintain good hydration (a singer should alswyas get enough water to maintain good hydration, anyway).

My usual recommendation, based on experience, is one 8-ounce glass of water per serving of alcohol. Note that, whatever the alcoholic beverage, a 1.5-ounce serving of hard liquor at 40% alcohol, a 6-ounce serving of wine at 10% alcohol, or a 16-ounce serving of beer at 3.75% alcohol (these numbers are approximate; serving sizes and alcohol contents will vary, but within acceptable limits), all contain the same amount of alcohol (.6 of an ounce), so the same amount of water will counteract their dessicant effects. If you are observant, you will find the amount of water that works for you.

Dehydration is one of the main contributors to hangovers, too, so getting enough water will mitigate those as well. Now, this answer doesn't address the immediate effects of alcohol on control of the voice. Singing drunk is a problem for the same sorts of reasons as driving drunk (though fewer people get killed). Your judgement and attentiveness are impaired. You are more likely to oversing and less likely to think about proper technique. Once in a while, this will not be a problem, as your body will have the opportunity to heal from any damage you may do. Do this too much, though, and you will find the damage compounded.

So remember the key: MODERATION.