Call the licensing agency and ask them.
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In most instances having a misdemeanor conviction will bar you from getting a gun license but check with you local police & licensing agency
The advice I have given does not bind the parties in any manner and is merely given as a courtesy.
In each County in New York State, pistol permits are issued by one (or more) designated County Court Judges. If you have a pistol permit and are charged with a misdemeanor or felony (including a DWI) will trigger a review of your permit. This may lead to a hearing to determine if your permit will be revoked. In some instances, such as Domestic Violence or other offenses where Orders of Protection are issued, you guns will be seized and held by law enforcement pending the outcome of the case. Your permit will not always be revoked in every instance.
All of this is to say that a misdemeanor DWI conviction will be a factor in reviewing your application, but may not serve as an absolute bar. Candidly, some New York Counties are far more lenient in issuing permits then others,