Dec - Jan trip clothing questions

Your boots sound as if they’d be fine, but I would re-waterproof them before I left. Your clothing plans sound good too, except I found out last winter that my puffa coat from Lands End was not waterproof in a heavy rain, so I would make sure my coat was definitely waterproof. If you normally wear wool dresses with tights in cold winters then you should be fine, but be aware there can be a big difference in temps from the south to the north, so it also depends on where you plan to go. And yes, I usually need to take off a layer or 2 when I go inside so layers are a good way to go.

The inside of buildings will be warm so you may be wanting to strip off when going into shops, restaurants, museums, galleries etc.

I love visiting London in January because the hotel prices are low and so are the crowds. My first few January visits, I employed the layering technique, but always felt like I was toting a ton of layers in my bag or feeling like the Michelin man with all my layers on.
So for the last few trips, I took the advice of another forum poster and brought a warm winter coat under which I wore a 3/4 sleeve top and a cardigan. I found it was much easier to just take the coat off when entering the underground or a shop or a theater.

Enjoy your visit!

I do what Acccidental Southerner does after a winter trip where I felt like I had to strip everything off indoors and was sweating on the metro. I did a Christmas market trip last December and wore a warm waterproof parka from Eddie Bauer. That and my waterproof Chelsea boots kept me warm and dry. I did use 32 degree lightweight thermals from Costco, but I get cold very easily. Don’t forget a scarf, hat and gloves.

Whether the inside of places is warm depends very much on the place and your perception of temperature. I am often too cold in cafes and restaurants in winter. A lot have doors that open directly to the outside so you get an icy blast every time someone comes or goes. But then you’ll find some places that are very warm, so as ever layers really are key.

If it’s chilly I wear a thermal sleeveless vest (we call it. I think it’s known as a tank in the US? It’s underwear anyway) from the Uniqlo heattech range under absolutely everything. You can take it off in the toilet if you really need to.

That sounds like a good plan, @Accidental Southerner! May I ask what length your parka/coat was?

Also...looking at past weather, I see a lot of temperatures in the 50s. I assume that's a cold-feeling 50s? Little sun, damp cold that goes through your clothes?

Yes! Be prepared for finding it really cold and damp if you're used to Texas. Lots of the climate is coming in from the Atlantic that time of year and it can be pretty chilly and wet

Like others have said above, don't go mad like you're traversing the Antarctic if you're around London. Further up north you go and the more out into exposed parts of the country you'll need to dress for it a bit more.

I like a good hat. I prefer a beanie. Makes a big difference to how warm I am even if I'm not really properly dressed for weather otherwise.

Waterproof boots are overkill for town for me, but that is personal.

That sounds like a good plan, @Accidental Southerner! May I ask what length your parka/coat was?

Mid thigh. It’s a lightweight coat that I don’t mind carrying over my arm indoors, yet it is warm— rated down to the 20s Fahrenheit. I have a warmer coat rated to below zero F but that would be overkill for London.
Agree that hat, scarf, and gloves are key.
I usually take a pretty silk scarf because I like the way silk is lightweight, warm, and oh so soft. But that’s just me!