Argh, I had a nice long response typed up to everyone and then my phone died and I lost it!
I'm glad to know I'm not the only one who thinks this dress code sounds challenging. I agree that asking for formal at an event with no climate control is... risky? insensitive? Their announcement suggests that guests check the forecast and bring layers, so I guess they're comfortable with people wearing reasonable footwear and outerwear. I hadn't considered the mountain-as-theme aspect that cjh's link describes, but that does give me something to go on.
As to venue, it's not terribly rugged: grassy meadow, gravel paths, gazebo by a pond, that sort of thing. April's description of fall events in the northeast is 100% in line with my experience. Last year we did a birthday party camping trip in White Mountain National Forest the last weekend in Sept. We planned for frosty mornings and then it was sticky hot, 80s and humid the whole time. Never even put on our jackets! The year before that, same dates, I attended an anniversary party at a northern VT campground and it rained the whole time and never got above 50°F. Wore a raincoat all day, even under the tent, because it was too cold to take it off. Give me a casual event any day, so I can just dress for the weather and be done with it.
If it ends up being hot, I have a two-piece dress, navy blue raw silk, that could be a good fallback, but it feels a bit plain? I don't really want to buy accessories just for the sake of adding bling. And I'd have to deal with figuring out hosiery and footwear. I'm coming to terms with the fact that I don't like the look of most women's dress shoes, or the feel of most hose; leaning menswear would be easier for me -- dressy chelsea boots, oxfords, wingtips, brogues... but not with a dress, so that leads me to pantsuit/tuxedo options.
I'm in love with the look of the CM trousers below -- the texture, colour, silhouette -- and have two different sizes on order to try (reviews say they run large, but how large?). Maybe they skew too office-y, but I can picture them styled with a silky cami/tank of some sort, or a fitted button-up waistcoat. I'm going to try them on with my navy raw silk tank, and also the floral cami below. I like the idea of them with the black eyelet tank as well, but maybe that's too casual, and too seasonally confused even for September in New England? I wish CM had a coordinating topper in the same fabric, but maybe just a cropped blazer/short drape-y trench would be fine?
I'd love to be able to shop my closet for events like this, but formal is so rare in my world that I don't really have the right stuff on hand. Rent the Runway is maybe a possibility, if I can't find something appropriate that I think I'll be able to remix and re-wear in the future. But not being able to do alterations might make it just as tricky and time-consuming as retail. (DH would love to be able to rent, as he hasn't needed to wear a suit in over a decade and doesn't have one -- but he's such a slim build I doubt he'll find something that fits well without alterations.)
Oh, and to everyone who mentioned alpine/Tyrolean -- that is remarkably spot-on, actually. The groom (my cousin) spent a good part of his 20s living and working in Austria. I don't think he'll be wearing his lederhosen, but he could surprise us.