In his book, Sport Science, Peter Brancazio, with such projectiles as baseballs and golf balls in mind, writes: Everything else being equal, a projectile will travel farther on a hot day than on a cold day, farther at high altitude than at sea level, farther in humid than in dry air. How can you explain these claims?

The air drag experienced by the object in projectile motion depends on the density of the object in which the object moves. If the medium is highly dense, the resistance offered by the medium to the moving object is significantly large such that the range of the object decreases.
On a hot day, the same amount of air occupies more volume relative to when it’s a cold day. This decreases the density of the air relatively, together with the air resistance experienced by the object. The lesser air resistance on a hot day allows object to go a larger range relative to the same on a cold day.
At the higher altitudes, the air is less dense, and therefore the air resistance offered to the moving object is relatively less as compared to the sea level. The less air resistance allows the projectile to go a higher range.
Humid air contains more water molecules than the oxygen and nitrogen molecules. The water molecules being lighter than the oxygen and nitrogen molecules accounts for the lower density of the humid air. The air resistance experienced by the object in humid air is relatively less and therefore the object can travel larger horizontal distance in it.