Praise be to Allah.
Images of animate beings that are drawn by hand or engraved on wood or copper, or made out of plaster, are undoubtedly prohibited and are included in the texts that warn the image makers.
What is mentioned above about images that are made to last and will remain for a long time is a matter concerning which there is unanimous agreement among the scholars. As for making images with materials that do not last for long, such as images made out of dough, melon rinds or sweets, we do not find any discussion of them in the books of fiqh, except among the Maalikis and Shaafa‘is. We find that there is a slight difference of opinion concerning that among the Maalikis, but the majority are of the view that such images are prohibited. As for the Shaafa‘is, they regard it as prohibited to make them, but some of them regard it as permissible to sell them! Ar-Ramli – who was one of their senior fuqaha’– refuted the view of those who said that that was permissible.
A similar argument may be applied to images made out of snow, as mentioned in the question.
‘Ulaysh al-Maaliki (may Allah have mercy on him) said:
It is prohibited to make images that meet the conditions mentioned above, if they are made to last, such as those made out of wood, clay, sugar and dough, according to consensus. That also applies if they are not made to last, such as those made out of melon rinds.
Minah al-Jaleel Sharh Mukhtasar Khaleel (3/529)
Abu’l-‘Abbaas Ahmad as-Saawi (may Allah have mercy on him) said:
There is a difference of opinion concerning that which is not made to last, but the correct view is that it is prohibited.
Haashiyat as-Saawi ‘ala ash-Sharh as-Sagheer (2/501)
Ahmad an-Nafraawi (may Allah have mercy on him) said:
If the image is made in a complete form and has a shadow, such as if it is made in the image of a wild animal or dog or human, and it is placed on a wall or on the ground, then that is prohibited, because it is a complete image, whether it is made of something that lasts, such as stone or wood, or of something that does not last, such as if the image of a wild animal or horse is made out of dough or sweets that do not last for long.
Al-Fawaakih ad-Dawaani (2/315)
In Haashiyat Qalyoobi (3/298) – which is a Shaafa‘i book – it says:
It is prohibited to make an image of an animal, even if it is in a form in which a living being could not survive and there is nothing equal to that in real life – as we have seen above – or it is made of clay or of sweets. But it is valid to sell it, and it is not prohibited to look at it or leave it alone (and not destroy it). This was stated by our Shaykh ar-Ramli, but our Shaykh ar-Ziyaadi disagreed with him on the last two points and regarded those actions as haraam.
What seems most likely to be correct is that with regard to the prohibition on making images there is no difference between that which is made to last for a long time and that which is not. It was narrated that the mushrikeen during the Jaahiliyyah used to make images that they worshipped instead of Allah out of dates, then if they got hungry they would eat them! This confirms that there is no difference in terms of the name or ruling between images that are made out of material that lasts and those that are made out of material that does not last.
Our contemporary scholars gave rulings that are similar to the view that is most likely to be correct according to the Maalikis and Shaafa‘is.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said:
The images that are prohibited are images such as the following: where a person makes out of dough or plaster or any other material something in the image of a human being or an animal. This is haraam.
With regard to trees and the like, there is nothing wrong with (making images of) them, according to the more correct view, which is that of the majority of scholars.
Sharh Riyaadh as-Saaliheen (6/207)
Shaykh Saalih Aal ash-Shaykh (may Allah preserve him) said:
It is confirmed in linguistic terms that the idol is graven image, i.e., something that is carved or shaped in the form of an image. As that is the case, then an idol may be made out of either stone or wood or dough or dates, and so on.
Sharh Kashf ash-Shubuhaat (tape no. 8)
With regard to the questioner saying: “As far as I know there is no creature that looks like a snowman”, even though this is correct in and of itself, it does not alter the Islamic ruling. There is no such thing as a man made of copper or wood or plaster or dates. The point is that they make the image of an animate being out of these substances, then they give it a nose, two eyes and a head – this is the reason for the prohibition. If they were to make out of those substances something that has no soul (an inanimate object), there would be no objection. Or they could make an animate object without giving it a head.
In addition to this clarification of the ruling, the scholars also stated that it is prohibited to make fantasy images of men and animals, except in the case of toys for children.
In al-Mawsoo‘ah al-Fiqhiyyah (12/111) it says:
The Shaafa‘is stated that fantasy images of humans or animals are also included in the prohibition. They said: That is prohibited, such as a man with wings, or a cow with a beak, things that do not exist in real life. The words of the author of Rawd at-Taalib suggest that there may be some views that permit that.
It is clear that this discussion has to do with things other than toys for children. It is narrated in the hadith of ‘Aa’ishah (may Allah be pleased with her) that among her toys was a horse that had two wings, and that when the Prophet (blessings and peace of Allah be upon him) saw it, he smiled broadly.
In fact, if it were to be said that such things are more emphatically prohibited than images of real creatures, as is the view of some of the scholars, that would not be far-fetched.
Al-Maawirdi (may Allah have mercy on him) said:
There is no difference in the prohibition on images of animate beings between images of humans and of animals, or between those that are made to appear pleasing to the eye and those that are made to appear ugly, or between those that are huge and those are very small, if they are images of real animals.
As for images of animals that have never been seen (fantasy creatures), they come under the same ruling, such as images of a bird with a human face, or a man with the wings of a bird. There are two views concerning the prohibition on such images. The first view is that they are prohibited and, in fact, are more emphatically prohibited because it is introducing innovation into the creation of Allah, may He be exalted, and because the Prophet (blessings and peace of Allah be upon him) said: “He [the image-maker] will be instructed to breathe life into it, and he will never be able to do so.”
The second view – which is the view of Abu Haamid al-Mirwazi – is that they are not prohibited, because they are more like artistic decoration than images of living beings.
According to the first view, it is prohibited to make an image of a human face without a body, but according to the second view, it is not prohibited to do so.
Al-Haawi al-Kabeer (9/565)
To sum up:
It is not permissible to make images out of snow, even for fun. Allah has given people plenty of leeway to make whatever they want of images of things that are inanimate, such as trees, ships, fruits, buildings and the like.
And Allah knows best.