Your needs will be determined by the length of time you plan to be in the rain and your budget. You will need a jacket, pants, and shoe protection . Some cyclists wear a helmet covering all winter, while others use them only when it rains hard since they are effective in holding in the heat. Special cycling jackets have underarm zippers to help vent your internal heat. A helmet should be standard equipment.
Many cyclists choose ear coverings for the cold days.
Those can be anything from the fancy cycling ear coverings that fit under helmets to a simple hair band found in a pharmacy. The key is to keep ears warm while allowing cyclists to see and hear well and turn their heads easily. Gloves or mittens are effective in protecting from the wind and rain. Waterproof gloves allow hands to stay warmer since they will be dry and out of the wind. Mittens should not interfere with your braking ability, but some cyclists choose them because they can keep hands warmer than gloves.