Try this link:
It lists the basic contact info for the parks and includes a blurb that says "If you’re looking for a unique and scenic location for your next party, meeting, a wedding or other ceremony; consider one of the venues in the Olmsted Parks: Marcy Casino, Parkside Lodge, Cazenovia Casino, The Rose Garden, Japanese Garden"
I think you might be able to reserve this through the historical society. Just double check though about volume, I believe it is only outdoors (no indoor backup) and ceremonies of less than 50. I am not sure if this has changed though. Good Luck!
Honestly it was sort of expensive, and it can be pretty but only during a small window of weeks. It was booked up 1.5 yrs in advance last year. And it's like a wedding chapel. One couple in for their time block, next wedding in for theirs. And they charge separately for picture taking time!!! Also, I know it was badly damaged months ago. Wonder how much work they've done on it since?
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