Baby ice dog

[hijinks at UTARLG.UTA.EDU]

I've been listening to T&M for at least 15 years now.  And I still am not
sure what Baby Ice dog is about. It seems that it's about plunging someone
troublesome/unfaithful into ice.  But I dunno fer sure.  Then we get this:

They'd like to make it with my big black dog
But they just don't know how to ask
You know they'd like to try anything that comes into your mind
Oh freeze  on freeze on freeze on bone to bone

What is up with the dog? Is it a metaphor (ala Jim Morrison, when "calling
on the dog" is a reference to god)? Why the shift in line 3 from third to
second person (also a typical Morrison move, ala "Words got me the wound,
and will get me well again/If you believe it")? Is the supposed woman
really a dog all along, and we see the reversal here (ala Zeppelin's Bron
Y Aur Stomp)?

Or what?

--tjr