If the permit says "license to carry pistol is hereby granted" then it is valid throughout the state as a carry permit. NYS PL 400.00 (licensing) states
6. License: validity. Any license issued pursuant to this section shall be valid notwithstanding (in spite of) the provisions of any local law or ordinance..... A license to carry or possess a pistol or revolver, not otherwise limited as to place or time of possession, shall be effective throughout the state, except that the same shall not be valid within the city of New York unless a special permit granting validity is issued by the police commissioner of that city.
So if the permit is a CCW permit it is valid throughout the state and may not be infringed by any local law. There are no provisions in any NYS law requiring the gun be carried in any other form than concealed and loaded.
Now for the reality... many judges will advise a licensee that they may not carry the gun going to or coming from the event. In lower NY counties a wide berth is given to this and people generally don't have a problem. But we are seeing a lot of anti-gun sentiment from the LO in a number of counties in Western NY. The laws have become so convoluted in many states that honest law-abiding people aren't sure what to do.