Cold air>>>> Cold air is MORE DENSE than warm air, more air molecules per given space, less water molecules in that air, water molecules do not have any substantial effect on the bullet.The more air the bullet must move through, the more drag on the bullet, the bullet doesn't fly as far, or as flat.
Dense, or cold air is good for airplane wings, normally aspirated engines, but bad for bullets.
All things being equal....Hypothetically, a bullet sighted in at 100y will drop 58" on a 60 degree day but only drop 56" on a 90 degree day.
Warm air....less dense, less air molecules in a given space, more water molecules.
Less air molecules for the bullet to move through, less drag on the bullet, the bullet fly's farther and flatter.
The same can be said of barometric pressure.....HIGH barometric pressure...MORE air molecules in a given space, bullet has more air molecules to travel through, more drag on the bullet, bullet doesn't fly as far or as flat.
LOW Barometric Pressure..... LESS air molecules in a give space, bullet has less air molecules to move through, less drag on the bullet, bullet fly's farther and flatter.
Elevation.... HIGH Elevation, less Barometric pressure, LESS, air molecules per given space, LESS air molecules for the bullet to move through, less drag on bullet, bullet flys farther and flatter.
LOW Elevation.... MORE air pressure, more air molecules per given space, more air molecules for bullet to move through, more drag on bullet, bullet doesn't fly as far or as flat.
So, let's recap: Assuming you're sighted in and dead on at 100y. at a certain atmosphere, then, things change,it gets:
HOT(er)>>>> Bullet will hit HIGH(er) at 100y
COLD(er)>>>> Bullet will hit LOW(er) at 100y.
Your dead on at 100y and the Barometric Pressure:
INCREASES(High Pressure)>>>> Bullet will hit LOW(er) at 100y
DECREASES(Low Pressure)>>>> Bullet will hit HIGH(er) at 100y
Your dead on at 100y and you: (Above Sea Level)
INCREASE your Elevation>>>> Bullet will hit HIGH(er) at 100y
DECREASE your Elevation>>>> Bullet will hit LOW(er) at 100y
This meaning you, the shooter increases or decreases your elevation in regards to mean sea level, nothing to do with your sights on the firearm.
Hope this helps...Merry Christmas!