Global warming is amplified in the Arctic. However, numerical models struggle to represent key processes that determine Arctic weather and climate. To collect data that help to constrain the models, the HALO-(AC)3 aircraft campaign was conducted over the Norwegian and Greenland seas, the Fram Strait, and the central Arctic Ocean in March and April 2022. The campaign focused on one specific challenge posed by the models, namely the reasonable representation of transformations of air masses during their meridional transport into and out of the Arctic via northward moist- and warm-air intrusions (WAIs) and southward marine cold-air outbreaks (CAOs). Observations were made over areas of open ocean, the marginal sea ice zone, and the central Arctic sea ice. Two low-flying and one long-range, high-altitude research aircraft were flown in colocated formation whenever possible. To follow the air mass transformations, a quasi-Lagrangian flight strategy using trajectory calculations was realized, enabling us to sample the same moving-air parcels twice along their trajectories. Seven distinct WAI and 12 CAO cases were probed. From the quasi-Lagrangian measurements, we have quantified the diabatic heating/cooling and moistening/drying of the transported air masses. During CAOs, maximum values of 3 K h-1 warming and 0.3 g kg-1 h-1 moistening were obtained below 1 km altitude. From the observations of WAIs, diabatic cooling rates of up to 0.4 K h-1 and a moisture loss of up to 0.1 g kg-1 h-1 from the ground to about 5.5 km altitude were derived. Furthermore, the development of cloud macrophysical (cloud-top height and horizontal cloud cover) and microphysical (liquid water path, precipitation, and ice index) properties along the southward pathways of the air masses were documented during CAOs, and the moisture budget during a specific WAI event was estimated. In addition, we discuss the statistical frequency of occurrence of the different thermodynamic phases of Arctic low-level clouds, the interaction of Arctic cirrus clouds with sea ice and water vapor, and the characteristics of microphysical and chemical properties of Arctic aerosol particles. Finally, we provide a proof of concept to measure mesoscale divergence and subsidence in the Arctic using data from dropsondes released during the flights.