Praise be to Allah.
If the snowman does not have clear facial features such as eyes, a nose and a mouth, and it is merely a three-dimensional figure with no features, like the scarecrows that farmers set up to scare away birds, and signs that are put on roads as a warning of roadworks or construction, then there is nothing wrong with any of that.
Similarly, there is nothing wrong with what children do for fun, because such figures are not usually treated with respect (unlike statues and idols) and it is well-known that children have a psychological need to play and have some fun and excitement, especially in places where snow only falls on rare occasions.
But if the snowman has clear facial features, then the majority of scholars are of the view that it is prohibited, because of the general meaning of the prohibition on making images, which has been explained in detail in question no. 146628. A similar ruling applies to figures that are made out of dough and other sweets, and so on.
But that is undoubtedly less serious than images that are made to last and are less likely to be treated with disrespect than snowmen. It is well-known that prohibitions are of varying degrees and it is well-known that the general meaning of shar‘i evidence prohibits images.
What matters in the case of images is the head. If the head is cut off or the features are erased, the prohibition no longer applies, as al-Bayhaqi (14580) narrated from Ibn ‘Abbaas (may Allah be pleased with him) that he said: The image is the head; if the head is cut off it is no longer an image.
Ibn Qudaamah (may Allah be pleased with him) said: If the image is nothing but a body without a head, it is not included in the prohibition, because that is not an image of a living being. End quote from al-Mughni (7/282)
In Sunan Abi Dawood (4158) it is narrated that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Jibreel (peace be upon him) came to me and said to me: ‘I came to you last night and nothing kept me from entering but the fact that there were statues at the door .... So tell someone to cut off the heads of the statues that are by the door of the house, so that they will become like trees ...’” And the Messenger of Allah (blessings and peace of Allah be upon him) did that.
Al-Mubaarakfoori said in Tuhfat al-Ahwadhi (8/73):
This indicates that if the shape of the image is changed, by cutting off the head or dismantling it so that there is nothing left but a vague and unclear shape, there is nothing wrong with that.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
If the image is not clear, i.e., if it has no eyes, nose, mouth or fingers, then it is not a complete image and it is not competing with the creation of Allah, may He be glorified and exalted.
And he said:
As for the issue of that of which no clear image appears, even though there are limbs or a head or neck, but there are no eyes or nose, then there is nothing wrong with it, because it is not competing with the creation of Allah.
End quote from Majmoo‘ Fataawa ash-Shaykh (2/278)
And Allah knows best.