Question: If fire annihilates the Dead, why are they such a threat? Wouldn't Jon Snow just ask to borrow Khaleesi's babies for an afternoon?

I'm aware that Dany is the only one who can control her dragons. 

My point is this: Jon Snow is trying to unite houses, tribes, and kingdoms the world over against a common enemy, continuously reminding all that will listen that they have never been up against a force so formidable as the White Walkers and the Army of the Dead, and that only he has seen what the Night King can do, and that if the world of the living is to endure, we must rally every warm body against them. 

But I fail to see the magnitude of such a threat in a world where one of its residents can control a weapon that administers a method of death (on a semi-mass-destructive scale) that happens to be the exact bane of such a potential threat. 

Why is Jon Snow so concerned with boots on the ground and global cooperation when it seems that one couldn't come up with a better antidote to the walking dead than dragon-fire?

Answer: 
**Spoiler alert**

This question is answered in the leaked episode S7E6.

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>  In S7E6, as Daenerys goes to save Jon Snow who is stuck north of the wall, the night's king takes one of the dragons down with a spear, and very easily. The dragons might have killed huge numbers from the army of the dead, but with the night king being able to kill them with one blow, if they started a war with the army of the dead using dragons only, the three dragons will probably die before being able to kill all of the dead, and the army of the dead will end up having three additional dragons.
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Dany knows Jon wants her dragons but right now they are too valuable as an instrument of war or simply as a show of force in taking the iron throne. Plus she views them as her children and is very protective.

Daenerys' dragons will eventually help Jon Snow and the North against the white walkers but I don't believe it will be as simple as flying over their armies and breathing fire to melt the dead away. The dragons are essentially flying lizards and are cold blooded animals. The temperatures north of the wall would be too hostile an environment for the dragons to be as effective as we have seen thus far. While I understand that their is a magical element so it is plausible for the dragons to endure the cold but if there are no repercussions in bringing them North it will be a huge flaw in the story and we all know nothing is that simple in this series.