My "turn out" is just a small pen attached to their stall. If your donkeys come to you easily, I wouldn't be too worried about pasture or pen size. If they won't come to you, chasing them around a several acre pasture could be a real pain
I have a mini donk that I leave pastured with my quarter horse mare. I have 2 stalls one large one for the mare and a small one for Mr Donk, but he prefers to stay with his lady friend in the big stall. The stalls open to the pasture and then can come and go as they please. With the first hint of rain or snow he high tails it to the barn. I have only locked them up during the worst of winter storms.
He was a pretty wild unhandeld stallion who kicked my dog in the chest as soon as he was taken off the trailer. With patience, a kind firm hand, and lots and lots of currying, (they loooooove) that, he is now a sweet heart that follows you anywhere and doesn't let you leave the pasture or barn with out an ear scratching first! (he will stand in front of you and not move till you scratch his ears) He is loved by all in the family! And now that he is used to the dogs, they play as well. :)