Can one make snow balls or a snow man on shabbos or this this boneh?
It would not be permitted to build a snowman on Shabbos. Concerning snowballs, some authorities are lenient for children, but some prohibit forming snowballs, and this would appear to be the more mainstrem opinion.
First of all, it must be noted that there is no issue of muktzeh concerning snow, whether for snow that fell before Shabbos, or for snow that fell on Shabbos itself. As Mishnah Berurah (338:30) writes, rain and snow do not have the status of muktzeh for Shabbos (see also Darkei Moshe 337, concerning rain; Minchas Shabbos 80:56).
The main issue, it would appear, concerning the formation of snowballs and snowmen, is the question of boneh (building). As Rambam writes (Shabbos 7:6, cited in Mishnah Berurah 319:63), “One who gathers one part to the other, and sticks everything together until they unite, this is similar to boneh.” As Rav Shlomo Zalman Auerbach noted (Shluchan Shlomo 314:4), This would apparently apply to the formation of snowballs (see also Mekor Chaim 320:9).
However, there is room to distinguish the formation of something new out of many small pieces, such as the process by which cheese is formed (which is the halachah that Rambam is dicussing), and the formation of a snowball. As Meiri writes, the formation of cheese is a creation out of small pieces, which can hardly be called cheese. Forming a snowball, rather than being an act of creation, is only an act of giving form to something.
This distinction has been made by Be’er Moshe (vol. 6, no. 30), who adds that a snowball has a very transient existence, which provides another reason to distinguish it from the creation of cheese.
Yet, even Be’er Moshe concedes that one may not create snowballs on Shabbos, because in their formation one cannot avoid crushing the snow (by applying pressure to it), causing some of the snow to melt but one’s direct application of pressure. This is forbidden on Shabbos (Shulchan Aruch, Orach Chaim 320:11), and Be’er Moshe therefore concludes that for adults it is forbidden to form snowballs, yet he is lenient for children.
Concerning snowmen, Be’er Moshe has no doubt that it is prohibited, yet does not give the reason for this. Presumably, he saw the snowman as a type of sculpture, which may not be made on Shabbos. However, others place the issues of snowballs and snowmen together.