There is a complete 'Adenium' group where people might be able to help you better - though I am sure there are plenty of Desert Rose growers among the Cactus and Succulent lovers who frequent this group.
I think cuttings will grow - but be sure to let it dry out before planting it and leave of the watering - I have never tried it. They also need to be potted in very very well draining soil so they they do not sit around with wet feet a lot.
These plants do not like to be wet and cold, that is frequently fatal to most kinds. So when it gets cold stop watering or reduce it to an absolute minimum - as a result the plant might loose it leaves that is normal new leaves will grow once it gets warm in the spring.
Once it gets warmer these plants want as much sun as you can give them and when it is warm and staying that way at night they can take quite some water.
