... let it snow, let it snow, let it snow. I wish that was the local weather report, but it's been all but tropical here in Wisconsin of late. A few daring souls are still ice fishing and playing pond hockey on the shallow lakes that have a little ice, but almost all the lakes are, well, water.
Instead, the lyric provides what looks like an example of degrammaticalization. Grammaticalization is the process whereby words and forms take on more grammatical functions, like going to becoming a future tense form gonna. (Wikipedia has a reasonable summary here.)
Crucial to many views of how this process works is the claim that it's unidirectional -- things move only from less grammatical to more grammatical, like free word to clitic (words that reduce phonetically and lean on 'host' words, basically, like I am to I'm) to prefix or suffix, but never in the reverse direction. The literature on language change contains a growing set of counterexamples to this -- enough that unidirectionality is pretty much dead for a lot of us.
I wonder what the details of the history are, but it sure looks like the above sentence is another one: Main verb have could apparently once reduce and become a clitic in a lot of varieties of American English. Today, that sounds grossly ungrammatical to me and other speakers from various parts of the country.