I too agree with what others have said so far.... I would add -
Ducks will be fine as long as their are no sharp rocks, sticks which they can cut their feet on. Ducks are much more hardy than chicken's except for foot damage due to cuts.
Chicken's will flat out tear out any soft soil if they don't have enough
land to roam. So along with having a extra high
fence on the down hill side you will want them to have lots of room. If you give them only a roomy
chicken run area they will first kill off the ground cover and then begin to bring down the soil as they scratch for bugs. This won't happen if they are always moving - either because they have lots of land, or you are moving them, or other animals, like goats sharing the hillside, are moving them
Hillside solution - keep chicken's moving! Moving
chickens will do fine on hills.
Regarding milking cows - if you considered a smaller old-world breed such as Dexters they can handle hillside climbing, and they too will make horizontal cow walks for themselves over time.