There are three ways of laying out the four elements. If you choose to have Fire at the top of a + the element opposite can be any of the other three, and then the left and right positions are basically symmetrical and don't create more variation.
The layout you are talking about, the one with Water opposite Fire is the one aligned with Astrology. The actual hot, wet, cool and moist notions apply to the seasons dominated by those elements. Spring, dominated by Air (associated with rapid change) is wet and warm; Summer, dominated by Fire is hot and dry; Autumn, dominated by Earth, is dry and cool; Winter, dominated by Water, is cold and wet. This is true at least at the latitudes of the Classical Ascendancy.
Farther away from the Equator, Autumn is wet and Winter is dry, so Winter is associated with Air and placed opposite Summer associated with Fire; while Autumn is associated with Earth and placed opposite Spring associated with Water. The strong association of Winter with Air is common in northern cultures with festivals of light at midwinter when the air is exceptionally clear, and the alternation of temperate wet and extreme dry seasons, can be found in some Celtic and Teutonic traditions.
The arrangements opposing Fire with Earth are more common in cultures less dominated by either of these forces, because the actual substances physically, visibly arrange themselves that way. The heat of fire rises, and Earth falls through both Air and Water. This is the elemental arrangement that has become more popular over time, and is used, for instance in Jungian type theory, European racial stereotyping, and Wiccan geographical associations.