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I have heard of this before. As a matter of fact we know a couple that got married at a covered bridge in NH. Their plan was to see every covered bridge in New Hampshire and when they were done get married at one of them, which they did.
All you need to do is chose which covered bridge you want to get married at and contact the town where the bridge is located. Some towns are more receptive to this than others. But it should be just a matter of getting a permit. I believe it may be a Permit to Assemble, but I am not sure on that. You have every right to be there if it's public property, but to organize a group may require a permit.
Let us know how you make out!