In addition:

I use a "rain" cover on my helmet to make a warm air pocket there. Got a pair of ski goggles, cause the eyes get cold as speed.

You can buy a bicycle fairing. That will keep a lot of the wind off ya, but I would think it would be hard to keep clean.

If it is burning your throat, you probably should slow down. I went fast and hard on a beautiful sunny winter day last year and fried (or froze) my throat. I was in good shape from indoor track racing, but breathing that volume of cold air outside gave me a throat infection, and took me down for a week plus.

Note to self - don't go hard enough to freeze my esophagus when it is in the teens - even if it feels "warm" and sunny.