Monica, thank you for starting an interesting discussion. I'll try to take a more basic, perhaps over-obvious, approach to your questions. You had asked when to wear a long dress and a short one, and if there is a certain reason why the dresses are designed the way they are. You've gotten several answers talking about the "when," but to me, it seems far fewer concerning the "why." From my perspective, the different dresses are designed to flatter the woman's appearance and accommodate the different styling and flow of the different dances. Styling as I'm using it here refers to both the technical features of a dance, as well as its cultural history. Yes, you can generalize and say that the traveling dances – the ones in which dancers move around the room – call for long dresses, and the Latin and rhythm dancers – which tend to stay in one small general area of the dance floor – call for shorter ones. There are exceptions, of course: bolero, for instance, is a rhythm dance for which a well-chosen mid-length or long dress can be worn with great style.
Waltz, for instance, travels; and the traditional dress for the dance is the gown. The flowing fullness of the dress follows the rise and fall of the dancers, and swirls nicely during the many traveling turns made by the dancers. But the same dress would be a flop when dancing, say, a cha cha. The fullness so graceful in the waltz would either mask the actions of the lady, or perhaps exaggerate things like hip motion to the point of comedy. In some cases, the dress might even be a hindrance – a woman would be much better able to comment on that than I.
On the other hand, a short skirt, depending on the style, may flounce flirtatiously or emphasize the lady's legs.
As a guess, what occurs to me is that instead of saying long dresses are used for modern/smooth/traveling dances, and short ones for Latin/rhythm, it may be more accurate to say longs dresses are generally preferable in dances in which the dancers' lines or poses are more important? At least to me, it seems bolero calls for more dramatic poses than the other rhythm dances, which may explain why, IMHO, a longer dress works so well for it. A longer dress' drape, it seems to me, would help "complete," or fill out, some of the shapes/lines/poses, from a visual-aesthetic viewpoint. And shorter dresses for Latin/rhythm are preferred because, through flounce or exposure, they get more attention on the dance floor and accentuate the lady's movements?
Then there are the technical aspects of the dances. For example, International style modern (waltz, etc.) keeps the couple in closed positions, while American style allows them to open up and separate. International dresses may allow the lady to wear long, feathery and free-flowing things I believe are called boas. They wouldn't work in American style (speaking from experience) because when the couple tries to resume a closed position, the boas (and/or long scarves and similar floating "fluff") easily entangle the man's hand behind the lady's back, with results that are awkward for the dancers and fatal for the effect the fluff was suppose to be creating....
The history of the dances and their resulting fashions is more clear-cut. For instance, waltz originated in an era of long full dresses: Napoleonic and Victorian-era Europe. Certainly for the Victorians, it would have been shocking to see so much as an ankle exposed, so long dresses were required. And the dance that survived from period was the one designed to take full advantage of what long dresses had to offer. The Latin/rhythm dances, in contrast, originated in the hot, humid Caribbean, in which a formal ballroom gown would have been tortuous. Tango, with its roots in the slums and brothels of Buenos Aires, typically calls for a mid-to-long dress, but something more sensual than the waltz, and so on.
