From my reading of the various effects my current position is:
To examine this properly we need to determine if the dragon's breath is a magical effect (which would mean a narrow reading of the dragon's breath text would be appropriate).
Why is this important. For this we use the statement in the PHB (pg 7) about the rules:
Remember this: If a specific rule contradicts a general rule, the specific rule wins.
Exceptions to the rules are often minor. For instance, many adventurers don't have proficiency with longbows, but every wood elf does because of a racial trait. That trait creates a minor exception in the game. Other examples of rule-breaking are more conspicuous. For instance, an adventurer can't normally pass through walls, but some spells make that possible. Magic accounts for most of the major exceptions to the rules.
As a result the default assumption in reading/interpreting the rules has to be that if it's not magic then it follows the regular rules, unless the text of the effect states otherwise. Thus, if the dragon breath is not magic, it should be assumed to follow the regular rules for gas vapours and fogs unless it's text creates a specific exception.
So is it?
Answer: A dragon's breath weapon is not a magical effect.
Source: Sage Advice Feb 2016
Is the breath weapon of a dragon magical?
Ask yourself these questions about the feature:
- Is it a magic item?
- Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
- Is it a spell attack?
- Does its description say it’s magical?
If your answer to any of those questions is yes, the feature is magical.
Let’s look at a white dragon’s Cold Breath and ask ourselves those questions. First, Cold Breath isn’t a magic item. Second, its description mentions no spell. Third, it’s not a spell attack. Fourth, the word “magical” appears nowhere in its description. Our conclusion: Cold Breath is not considered a magical game effect, even though we know that dragons are amazing, supernatural beings.
Note: @gaynorvader said in the comments:
[A Green Dragon's breath] a supernatural ability, while not magical, doesn't necessarily obey the normal physical rules/natural laws
To address this, the MM (Pg 86) states:
Dragons are also magical creatures whose innate power fuels their dreaded breath weapons and other preternatural abilities.
The key word here is preternatural. The definition of preternatural (according to The Cambridge Dictionary) is
"more than is usual or natural"
with the example of:
Anger gave me preternatural strength, and I managed to force the door open.
Supernatural on the other hand is defined by The Cambridge Dictionary as:
caused by forces that cannot be explained by science
with the example of:
Ghosts and evil spirits are supernatural.
She is said to have supernatural powers and to be able to communicate with the dead.
So supernatural explicitly cannot be explained by science (like magic), whereas preternatural is simply more than is usual or normal (which may or may not be explained by science). We know that Dragon Breath weapons are not magical (from the SA column), so this reading would put the breath weapon in the category of "more than normal"
Next we need to determine what the spell Warding Wind (Elemental Evil Players Companion Page 23) does:
It hedges out vapor, gas, and fog that can be dispersed by strong wind.
The qualifier to the text here is that it can only do what a strong wind can do. This leads us to the question, what is a Strong Wind?
The DMG provides an answer (on Page 110):
A strong wind imposes disadvantage on ranged weapon attack rolls and Wisdom (Perception) checks that rely on hearing. A strong wind also extinguishes open flames, disperses fog, and makes flying by nonmagical means nearly impossible. A flying creature in a strong wind must land at the end of its turn or fall.
A strong wind in a desert can create a sandstorm that imposes disadvantage on Wisdom (Perception) checks that rely on sight.
So a key feature of a Strong Wind is that it disperses fog.
What is a "fog" and is it similar to the "gas" that the Green Dragon exhales?
There is not a specific definition of "fog" or "gas" in the game, however there are a number of locations in the PHB and the DMG that suggest they follow the same rules for dispersal.
We can clarify this by examining some of the effects that create fogs, gases and vapours.
First to be examined is Cloudkill (PHB pg 222):
You create a 20-foot-radius sphere of poisonous, yellow-green fog centered on a point you choose within range. The fog spreads around corners. It lasts for the duration or until strong wind disperses the fog, ending the spell. Its area is heavily obscured.
The fog moves 10 feet away from you at the start of each of your turns, rolling along the surface of the ground. The vapors, being heavier than air, sink to the lowest level of the land, even pouring down openings.
This spell description shows that we can equate fog with vapors as well.
Second on the list is Fog Cloud (PHB pg 243):
You create a 20-foot-radius sphere of fog centered on a point within range. The sphere spreads around corners, and its area is heavily obscured. It lasts for the duration or until a wind of moderate or greater speed (at least 10 miles per hour) disperses it .
This gives us an explicit exception to the normal Strong Wind rules by saying that for Fog Cloud it's fog can be dispersed by only moderate wind.
Next is Guards and Wards (PHB Pg 248):
Place stinking cloud in two locations. The vapors appear in the places you designate; they return within 10 minutes if dispersed by wind while guards and wards lasts.
But Stinking Cloud (PHB pg 278) normally creates a gas:
You create a 20-foot-radius sphere of yellow, nauseating gas centered on a point within range.
So this paragraph from Guards and Wards gives us direct corroberation that vapours are explicitly the same as gases.
Now we look at Gust of Wind (PHB pg 248):
A line of strong wind 60 feet long and 10 feet wide blasts from you in a direction you choose for the spell's duration. Each creature that starts its turn in the line must succeed on a Strength saving throw or be pushed 15 feet away from you in a direction following the line.
The gust disperses gas or vapor, and it extinguishes candles, torches, and similar unprotected flames in the area. It causes protected flames, such as those of lanterns, to dance wildly and has a 50 percent chance to extinguish them.
So a line of Strong Wind can disperse "gas or vapour". This gives good evidence that fogs, gases and vapours are intended to follow the same rules.
Now lets look at Storm of Vengence (PHB pg 279):
Finally, gusts of strong wind (ranging from 20 to 50 miles per hour) automatically disperse fog, mists, and similar phenomena in the area, whether mundane or magical.
This description explicitly gives us evidence that strong winds can disperse fogs, mists and other similar phenomena regardless of whether or not they are magical.
Up next is Wind Wall (PHB Pg 288):
The strong wind keeps fog, smoke, and other gases at bay.
This description explicitly groups fog as a gas.
Next on the list is the description of the Necklace of Adaptation from the DMG (Page 182):
Wondrous item, uncommon (requires attunement)
While wearing this necklace, you can breathe normally in any environment, and you have advantage on saving throws made against harmful gases and vapors (such as cloudkill and stinking cloud effects, inhaled poisons, and the breath weapons of some dragons).
What effects do cloudkill and stinking cloud add to our understanding?
Examining the excerpts we have from above for these two spell descriptions we can see that "fog" and "gas" are one and the same as "gases and vapours". This aligns with a plain reading of what a vapour is (that it includes a fog). From the Necklace of Adaptation description we also know that the breath weapons of some dragons are included in the definition of gases and vapours.
Combining that with what we have extracted from Cloudkill, Gust of Wind, Wind Wall, and Storm of Vengence (that gases, fogs and vapours are all the same) with what we have read in the Necklace of Adaptation description (that a strong wind effect can disperse gases and vapours), we can conclude that any effect that creates a strong wind can disperse gases.
As the Green Dragon's breath weapon produces gas, we can now determine that any effect that produces a strong wind can displace these gases.
Further evidence for this interpretation can be found in the layer actions of the Brass Dragon (MM pg 106):
A strong wind blows around the dragon. Each creature within 60 feet of the dragon must succeed on a DC 15 Strength saving throw or be pushed 15 feet away from the dragon and knocked prone. Gases and vapors are dispersed by the wind, and unprotected flames are extinguished. Protected flames; such as lanterns, have a 50 percent chance of being extinguished.
A similar lair action also exists for the Silver Dragon (MM pg 118)