Word Choice

The sentence is acceptable.

"Off of" when you mean "from" (formal) or "off" (less formal) is seen by many as incorrect and illiterate.

". . . if the ice and snow has melted off of the roof.

Shouldn't it be: ". . . if the ice and snow have melted off of the roof."

And if not, why not?

Could be 'has' if the ice and snow is regarded as one thing (frozen stuff), or 'have' if they are regarded as separate things. Both are OK.

I think I would add an additional comma after the word "permitting". It helps to separate the topic of the weather from the condition of the roof.

We have the roof demo scheduled for 1/2/18, weather permitting, and if the ice and snow has melted off of the roof.

I would also omit the words "off of"--substituting "from" instead.

So, I would write the sentence as...

We have the roof demo scheduled for 1/2/18, weather permitting, and if the ice and snow has melted from the roof.