My winter was like that -- rain and rain and more rain. That's one of the reasons we're not done with the Chicken Palace so that my chickens are living in a conglomeration of odd, rednecked housing.
All I can recommend is to increase the ventilation to the maximum possible without letting rain in and add dry organic material to soak up the wet. The coarsest material you can readily access to allow maximum airflow in the bedding. (Wish I could send you a bale of pine straw).
This is the tarp "porch" on my brooder -- it keeps the rain out of the wire wall without restricting airflow.
All I can recommend is to increase the ventilation to the maximum possible without letting rain in and add dry organic material to soak up the wet. The coarsest material you can readily access to allow maximum airflow in the bedding. (Wish I could send you a bale of pine straw).
This is the tarp "porch" on my brooder -- it keeps the rain out of the wire wall without restricting airflow.