Our experience in Spain is that vermouth is served in various glass designs, but always over ice.

Drinking wine over ice. I don't know about that. Must be a European thing

My friend who buys & sells wine for a living has no problem with wine over ice. And, as the Europeans pretty much "invented" wine, they have many centuries more experience than we do in NA.
A good book covering the history of wine is "Inventing Wine" by Paul Lukacs.
On average, we find inexpensive French, Spanish, Portuguese & German wines to be better than inexpensive NA wines.
Obviously, YMMV.

If people enjoy wine over ice more power to them. Its not something I would do.

By recipe, I use sweet Vermouth to make Manhattans. Simple Martini & Rossi, Dolin’s or my favorite, Antica Formula Carpano 1786. Often switching around the bitters used. I also experiment with different Amaro varieties. They tend to add more complexity to the drink. Some do not require any bitters to be added.

Cherry of choice is Luxardo.

In the last year or so I started drinking Negronis. I use Tanqueray Gin, Carpano Antica Sweet Red Vermouth, and Campari. I mix it like Stanley Tucci does - delicious!

https://www.youtube.com/watch?v=Srjk7qJ4PQ4

From "The Negroni: Drinking to La Dolce Vita": According to reliable lore, the cocktail was born when an Italian bartender responded to a customer's demand for a stiffer riff on an Americano cocktail (a much-tamer mix of Campari, sweet vermouth, and club soda). The patron, Count Camillo Negroni, had picked up a taste for strong liquor while working—true story—as a rodeo clown in the American Wild West, and gave his name to the resulting concoction.