The weather averages for Asbury Park for the entire month of October are a high of 65 and a low of 48. Donut and I have gone in the water there this time of year (with daytime temperatures in the 70s) and with climate change it’s felt like beach season has extended longer into the fall, although it’s also gotten rainier. If you’re coming in from outside the Northeast, you might want to pack a rain-appropriate coat/other light coat. You probably won’t need a winter coat unless we get a weird patch of weather.
If you’re wearing a dress/jumpsuit to the wedding you might want to bring some kind of cardigan/shawl for the ceremony (which will be quick but possibly windy because it’s on the water). If you’re wearing a suit your suit jacket will probably be warm enough. The reception is entirely indoors so it might get warm from the dancing, but there’s a wraparound deck if you need to get some air.