You would have to contact the town of Alington or whoever owns/services the park for this question. It's a beautiful area, and the views of Boston are really great on a clear day.
For parties under 50 people you can reserve tables for $50/$100 (resident/nonresident). For parties over 50 you can fill out a special permit a month in advance. That being said I just threw a bday party here for around 20 folks no reservations but it was on a Wednesday night. For something as special as a wedding, you might want to spring for the permit although I honestly can't imagine anyone coming by to yell "I object!" and shooing you away. Make for a good story though 😂 (edit to include link: https://www.arlingtonrec.com/info/facilities/area_info.aspx?FacilityID=13524&AreaID=14492)
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