Well, I can speak to what I wear to hike/ do trail work in the cold and the rain.
Footwear: Important, because nobody likes wet and cold feet. Something waterproof with good tread, so you don't go slipping in the mud. Paired with some nice, warm socks.
Body layers: Layers are the key to being out in the cold, so you can go up or down depending on how you feel. You never want to sweat while out in the cold, but you also definitely don't want to be shivering. Some sort of thermal base layer, thin but warm, is nice. Then you can add/substract sweatshirts, jackets, ect. (I find my legs never get cold unless temps get below freezing, but I also overheat easily when doing anything physical, even in the snow)
Outer Layer: A rain/water-proof shell can make all the difference in the rain. (Living in Washington, I spend a lot of time outside in the rain) I like to have light-weight, thin but waterproof jacket and rain pants, which can be easily stuffed into a backpack in case of rain, or if rain stops. A hood on the jacket is great, and I love rain pants with a full-zip side so I can put them on over my boots. (I don't own an umbrella because I like having both hands free)
Some kind of warm hat that covers your ears is great, people lose a lot of body heat through the top of their head. Being waterproof isn't neccessary if your coat has a hood. Some kind of brim (on the hat, or the coat hood) helps keep rain out of your eyes. Gloves are also a big plus, few things are as miserable as cold, wet fingers. I usually just go with insulated gardening gloves, with the rubberized palms. Great for gripping and flipping slimy rocks and logs. A spare pair of gloves in a pocket can be a godsend if your first pair gets soaked.
Some time and experimentation outdoors will hopefully let you figure out what combo of gear is best for you.
