A few questions
 

In short, I'll be in Tokyo over Christmas and New Year. My hotel doesn't offer breakfast, so I'm hoping someone will have the answers to these questions:

Is there anywhere especially good around the Asakusa area that sells Namagashi?
Is there anywhere/restraunt where you can be served a traditional Japanese breakfast?
Is there anywhere that does a tea ceremony in English? I've heard of this, but know no individual places.

What are you considering a "traditional Japanese breakfast"?

Rice, miso, tea with side dishes consisting of either fish or tamago, or even vegetables.

I don't think many people go out for breakfast, so chances are you will need to go to a hotel that serves breakfast. (Not necessarily stay there, but go there after you wake up.)

There are lots of hotels in Asakusa...

When I was in Tokyo a campaign was running promoting the eating of breakfast amongst working class.

Outside of the Denny's most places idea of breakfast was a coffee and two thick pieces of toast :)

So many places sell namagashi in Asakusa. That's what Asakusa is all about, "Good Ol' Tokyo". Just take a walk and you will easily find a few places.

For a cheap, full Japanese breakfast, I must recommend the gyuudon (beef bowl) places such as Yoshinoya and Matsuya. If you go to another hotel for breakfast, you could pay a few times more.
http://www.yoshinoya.com/menu/morningset/index.html

I tried to find a tea ceremony lesson in English near Asakusa but didn't find any.