Temperature, sun and wind can make huge variables when gearing for some winter fly fishing. Standing in 45-degree water can set you back pretty quickly too. You've heard it before, but I'll offer it again: layers, layers, and more layers. The most important way to keep yourself prepared is with the proper layers.
I like wearing a ball cap for fishing because the visor helps me with my visibility while I’m looking at the water. But I’ll always have a wool cap to switch on if I find myself cold. One of the best and fastest ways to regulate your body temperature is what you are wearing on your head. I recently found a decent billed cap with earflaps that can be pulled down. Certainly, the Elmer Fudd look has its own calling, but I’m not a slave to fashion while on the stream.
Alright Captain Obvious we know cotton socks don't work, so the best bet is a two-layer approach with your feet. I first put on a thin polyester-wicking sock. Overtop of the polyester sock I use a classic ragg merino wool sock. Bigger can be better, but make sure you can still get into your boots comfortably. If your socks are too thick and your feet are too tight your feet will be constricted in your boots and make your feet cold. What you are trying to accomplish is wicking away the perspiration from your feet with the polyester sock to the wool sock.
Side Note: Merino sheep date back to the 12th century from Africa and were crossbred with European sheep soon thereafter. The wool they produce is generally regarded as softer, very absorbent, and has great natural order control. Most importantly, even while wet, can provide warmth and insulation better than synthetic materials. It is the preferred wool and layering for many outdoor enthusiasts.
Legs and lower body
Again layers are the way to go. Keeping your legs and lower body warm while in the water is non-negotiable. A few years ago I ended up getting a pair of Simms Guide Mid Pants. These pants are made of fleece and provide greater insulation than cotton long johns. I would imagine you can get a decent pair of tapered fleece pants online that will do the trick. I like the tapered pants as they bunch up less at your ankles when you get into your boots. A few ways to approach this but I'd avoid the cotton sweat pants.
I generally have a three-layer approach to the upper body. I use a synthetic polyester base layer for wicking. I like the Under Armour mock long sleeves in a variety of styles but also have found some similar synthetic products at Walmart for a lot less. This offers a good base from the arms to the neck. The middle layers are your main insulators and are going to keep you warm. Fleece or merino wool always works well for me. I found a great fleece shirt at Walmart for $10 a couple of years ago and is my go-to whenever I head outside. I also have a warmer wool sweater for colder days. Just like your feet, you are trying to wick away any moisture and still keep insulated. The number of layers and type is really up to you and the temperatures you expect to encounter.
Finally for your upper body is a good outer shell. The key is something that will keep the wind from getting to you. With the layers you have already put on, a big winter coat is not the best step here.
A winter Windstopper shell that is water repentant is the answer. This is the place I would invest my money. I have an older Simms Windstopper jacket that works great and think I spent $200 over ten years ago. This one goes with me from October through May. Specific fly fishing wading jackets are usually cut short in length and thus avoid hanging into the water when you are wading. What you want is a sturdy windproof shell like the Orvis Tech Shell or Simms Freestone Wading Jacket. That thin nylon packable rain pullover probably won’t be enough. Once you are dressed and have your waders on you want warmth, but also upper body mobility too.
The other stuff
Fingerless gloves or mittens are a must. Plenty of good options made of wool, fleece and polyester for anglers. Leave the ski gloves for the slopes. Those HotHands Hand Warmers might be a backup option in your car or bag. Generally, if you are properly dressed and keep moving you’ll be in good shape.
You really should try all this gear on before you go to the stream. Adding a few more layers may cause some difficulties getting onto your fly fishing boots and waders. The holidays don't help either. No sense having all the right gear if you can't fit into your waders. I enjoy my fly fishing backpack this time of year with layers I am taking off or adding on. Finally, even if you don't think you'll need it, bring an extra layer to leave in the car.