Hello Ang, once my Adenium starts dropping its leaves, it is showing me dormancy time, so I just bring it in, and let it rest. It is a matured one, so it is just ready to sleep off the cold season. But we are still getting a wild swing of temps here, so I watch the overnight temps, once it nears the low 50's I prepare it for indoors, greater watering intervals to none. I do use insecticidal soap spray, before I bring it in, to make sure no critters on board, spraying any left over leaves topside and underside.
Each grower does differently, but I prefer to respect its dormancy and it comes back nicely in Spring, sometimes a tad slow, just depends on the ambiant temps. I would do any pruning in late winter to early Spring.