My parents are going to a wedding tomorrow morning in Brooklyn Bridge Park, which does not offer a covering in case of rain (according to the weather reports it will rain all weekend). The wedding is called for 10am with cocktails (I expect it would be mimosas, bloody marys and bellinis) first and the ceremony at 11am in the park and then back to the cocktail location for the reception. I’m assuming that when my parents and the other guests arrive the hosts will announce that the ceremony will be taking place indoors at the cocktails and reception location. But we'll find out tomorrow what happened.
It is so important that you have a rain plan if you’re having an outdoor wedding. Either reserve an indoor location or put a deposit on some tents. It is not worth the risk not to have a Plan B. After months of wedding planning you don’t want to let the weather cancel the whole day. And if you get wedding insurance check your policy because I think weather comes under the heading “acts of g-d” meaning that you won’t get your money back.