Friend of mine got married there a few years ago, sounded similar to what you described. Nice place, they do a good breakfast.
It was a little later in the year, but the groomsmen wore black tie, guests suits. I am fairly certain no one had any discussion about how anyone was dressed.
That said, if it were me, I'd wear a navy suit, white shirt with french cuffs, wedding tie, and a white linen pocket square. Black shoes, even if it is the country
Since you say you and your groomsmen already have black tie, well, the ceremony is after 6, black tie would be fine. I doubt if it would actually be any hotter than a suit. The location has little to do with it, it's the occasion. A wedding is not a horse show. I like a bit of rus in urbe, so why not have a bit of urbe in rus now and then. Particularly after 6.
What would you and your bride be more comfortable with? What do you want to see when you look at the pictures 10 years form now?