Icicles are a rather improbable natural phenomena, which is one reason that icicles are rarely found in nature.
For an icicle to form, there must be a source of fluid water that transforms into ice, meaning that there must be (relatively) warm water that somehow manages to freeze in the time it takes to drip down a brief distance. This is, on the face of it, a difficult thing to accomplish, since if there is water that is warm enough to be liquid and to flow, why would it then suddenly freeze?
That is why icicles are more a product of human habitation and building than they are of nature; and also why icicles are more a result of relatively warm times than truly cold times. Typically, icicles form when there is an object covered with snow that heats up to a temperature above freezing, while the air around it is still below freezing temperature. This is typically the result of a human structure, that is warming up because it is generating its own heat, or because parts of it are metal, stone or wood, materials that can absorb radiative heat quite well, even when the air around them is well below freezing. The snow melts, runs off the (relatively) hot roof and then quickly freezes while hitting the much colder air.
This is not to say that the same process doesn't occur naturally. The sun can heat up snow piled on a tree, or on a rock formation, which will then melt and refreeze in the shade. However, the icicles formed by natural processes are not usually the perfectly clear, cylindrical ones that we see hanging from roofs.