Wrapping outdoor faucets (hose bibs)

Getting mighty cold in central Texas.  Last couple days was 80+ degrees.
Got down to 40 at midnight last night and by 9:00 this morning, it was 32.
Going to be 17 degrees tonight, and 15 tomorrow night.  In fact, we may not
get above freezing until Saturday sometime.  It was a short summer.

Anyway, I went out and dutifully wrapped all our outdoor faucets; first with
a bath towel, then with two inch thick foam rubber, and taped it all tight
around the faucets.

But, I wonder why this keeps them from freezing.  Obviously, there is no
heat generated by wrapping them, and there is very little residual warmth in
the faucet / pipe stub.  A little residual warmth from the brick siding, but
that is all.  It seems to me that the bitter cold would soak through the
towel and foam rubber in a few hours.  Then, what good does it do to wrap
them?

I know it seems to help by wrapping the faucets, but I'm not sure why.  Any
ideas?

Bob-tx