Does smoking really affect my voice?

Yes.: Short term, the heat from the cigarettes can cause a pseudo-thermal burn on the vocal cords. This can cause edema of the vocal cords (reinke's edema). The vocal cords will vibrate differently and change your voice. Long-term smoking may lead to precancerous and cancerous changes to the vocal cords. This again will change your voice. If you smoke and have persistent hoarseness, you should see ent.

Yes: People vary in how much it affects the voice, and a lot depends on how much you smoke, how you smoke (deep inhalations, holding it for many seconds etc.), filtered or unfiltered, the amount of tar in your brand etc etc. If you ever heard maryanne faithful in her youth, and then heard what she sounds like recently, you will have a great example of how a beautiful voice can be ruined by tobacco.