In a program I've watched called Edwardian Farm, they use a temporary structure they called a 'Hay Rick' to store excess hay for the winter. There were already mushroom shaped concrete footings, that keep mice from climbing up from the ground onto the hay, they lay boards or sticks loosely across and place the hay on top, stacked. The illustration of a design they used show two men mounting a pole tent over the top, to be the roof. They chose to staple thatch directly to the top instead to help the structure shed water, but the middle top of the hay rotted. Link to video at beginning of the hay rick project:
https://youtu.be/UcBl4_2FJX4?t=1583
