QUESTION: What do I need to do to keep my chickens warm in winter?

Answer: There are a lot of variables to consider. I will try to keep it simple.
            
Chickens were originally derived thousands of years ago from the Red Junglefowl, their ancestors from Southeast Asia, and were later bred for hardiness. Some were bred to thrive in warm climates, while some have been developed to survive the coldest winters. Most common backyard chickens (the dual-purpose breeds) are fine down to very low temperatures, as long as they are not subjected to wind, wet, and cold - simultaneously. They can stand wind. They can tolerate wet. They don't mind cold. Combine two of these, and they may have a problem.
Eliminate two of them, and they should be fine.                                                                                                                                            
Feather-footed birds have an advantage in cold climates, since the feathering acts as a leg insulator. Birds with thick feathering are also cold-hardy.
Feeding your flock some scratch  in the morning and evening (not too much!) will help them generate enough heat to make it through the critical times. This is in addition to their normal rations.
Keep the coop floor covered with several inches of a suitable dry, fluffy bedding material. Pine shavings are okay (don't listen to the scare-mongers about this), or any quality bedding which doesn't soak up too much water. Keep it dry. Replace it when it gets too damp. You should have a composting area to break down this material, and use it in the garden, when spring comes around.
Prevent drafts, but do allow decent circulation. If possible, keep  the vents as far from the chickens as possible. Blocking all ventilation will cause ammonia build-up, which will kill chickens faster than cold!
Hang "heat lamps" above the roosts. We just use incandescent bulbs - not infrared or heating bulbs, which may become extremely hot. Be sure they are protected from contact with  the chickens or combustibles - like the bedding material. We tie ours so that they cannot be knocked down. You can use mug hooks, which are sturdier than cup hooks, but remember to add an insulated piece of wire, or thick rubber band, to hold it firmly in place.
YouTube videos
There are some great YouTube videos on various DIY projects for backyard chicken enthusiasts. I love the various home-made chicken feeders and waterers - especially the heated waterers.
If you have trouble finding poultry nipples, I have a few and can order more, if you need them.