Can you not make farms under ground?

Maybe also build a dining room and some personal rooms halfway up the mountain, too, so the people never need to run back to the village.

For extra "happiness" you could put some decorations on the mountain, too, to keep your cooks and butchers from getting too bored.

Also, unless you're using some crazy mods, all those animals will generate A LOT of bones and raw meats. So make sure you leave plenty of space (maybe on the bottom level of the mountain) for storage. And make sure you have enough wheat to feed them all. Remember that the skootenbeeten bird farms need to be fed the blue radish things instead of wheat; all other animals need wheat.

Or instead of building stairs, you could leave one edge of the mountain alone and use the existing grass pile to climb up and down. Save yourself a few pieces of stone/wood from making stairs.