Open Air deck on catamaran fast ferries between Split and Dubrovnik

All catamarans/fast ferries in Croatia have air conditioners (to the best of my knowledge).

Going out on deck as well as staying on depends on the capabilities of the individual vessel as well as weather conditions.

I traveled on numerous occasions when the weather was bad and the deck was not open for passengers. On some occasions, I remember open deck on some of the catamarans, like Krilo Star which is run by Krilo where passengers were sitting out enjoying lovely views (see some photos here: https://croatiaspots.com/island-hopping-croatia/)

Usually, outside decks are open for passengers when the ferry approaches and leaves the port, as the speed is slower so you can go out on the deck.

Most of the fast ferries have back and front open decks, usually not very spacious. These decks are used by the crew to navigate/manage the vessel.

In this video, you can see passengers sitting outside on the top deck.

This specific vessel is Krilo Star https://www.croatiaferries.com/krilo-star-kapetan-luka-catamaran-ferry/:

and Krilo Eclipse has an open-air deck at the back of the vessel, it doesn’t look very spacious, but still nice to stay on and enjoy the ride (weather & crew permitting):