Our goats have open fronted shelters. As we are in green belt, we have to be careful with concrete yards etc. so we have no frontage to he shelters .....does get muddy though. Earth floor inside, again due to the planning rules. Goats definitely need shelter from the wet weather, and so do donkeys.
Re the donkey: they are herd animals, and its usual to keep them in pairs. I know the donkey rescues will not rehome them unless you have two for this reason.
Two acres sounds a good size, but be careful you don't have too many animals on, especially in the wet weather ....it soon gets muddy, and churned up. Sheep especially eat right down , and the grass soon goes when they get going eating it, so I would probably split your field in half, so that one part could be resting, if thats possible. It will help conserve your grass a bit.
I have two goats, a llama, a pet sheep and a small pony on just under two acres, and I find that it gets very bare towards the end of the summer, and needs resting.