The chain isn't the only thing which can be damaged by snow...well, in the urban environment the snow isn't as bad as all the salt that is put on the roads. Winter riding requires regular maintenance, like rinsing & drying the bike off after a ride, using a winter lube for the chain (or a lighter lube more often), etc. Basically anything that can rust needs to be cleaned, including the frame if it is steel.

Fenders are preferred for commuting because without them, anytime you ride over water the bike's rear tire will pick up the water and throw it, so even if it is not raining but the roads are wet, when you arrive at the end of your commute without fenders, you'll have a wide stripe of water and mud up your back and on the rear of your helmet. Even with a waterproof jacket, if I ride one of my fenderless bikes I'm a little embarrassed if I go to the grocery store and walk around with a water stripe up my back, even though I'm completely dry. The front fender helps keep water and mud out of the chain ring and crankset.

Yes, what you linked to is a bike rack. They come in very handy when carrying work clothes for the commute, groceries, etc. The advantage to having a rack is that the bike carries the weight and not you, like if you only used a backpack, and your back won't get as sweaty like it will when there is a backpack on it.