If a person walks in the rain on Shabbat wearing a raincoat, upon returning home he may gently shake the water out of the coat.
One may hang a wet coat to dry on Shabbat, such as on a doorknob or shower rod, but it is forbidden to hang a wet coat near a source of heat, such as a radiator or fire. Firstly, the water on and in the coat may be heated on Shabbat, in which case one would have violated the prohibition of "Bishul" (cooking). Additionally, placing a wet garment near a source of heat has the effect of cleansing the garment, in violation of the prohibition of "Libun" (laundering).
Summary: One may gently shake out a wet raincoat on Shabbat; one may hang a wet coat to dry on Shabbat so long as he does not hang it near a source of heat.
See Munhat Ahava, Helek 2, page 412.
