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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Giant Wights with Large CrossBows like the one seen in S7E4-can slay a dragon. The top of the wall was a lot farther than Bronn was to the dragon with the Scorpion-shooting dragons with large bolts wouldn't be too hard for a giant.