Northern Fennoscandia (northern Scandinavia, Finland, and the Kola Peninsula) and the Altai region are where the oldest evidence for skis comes from. There are three difficulties:

1. Skis and skiing are probably older, and possibly much older, than the oldest evidence that has survived.

2. The oldest evidence is ambiguous.

3. Much of the evidence, in particular rock art, is difficult to date reliably.

The oldest evidence consists of the remains of ski-like objects, possibly about 8,000 years, from northern Fennoscandia. We don't know whether these are from skis or sled runners. It is generally though that the sled preceded the ski, and these remains are often interpreted as sled runners (Dresbeck, 1967).

The (probably) oldest rock art showing skiing is from Fennoscandia (Dresbeck, 1967; Kolpakov, 2020). The older skiing art is usually dated to about 5,000 to 6,000 years ago, but this dating is uncertain. The believed-to-be oldest petroglyph, the Rödöy skier (or Rødøy skier),

• https://jaypeakhistory.com/published-works/sticks-poles-a-ski-history/4500-years-ago/droppedimagec/

estimated to be 6,000 years old, is ambiguous. If skis are shown, they are remarkably long and curly skis, and might be a boat instead (Dresbeck, 1967). Other art, perhaps not as old, shows unambiguous skiers.

The Altai rock art is usually dated to about 4,000 to 5,000 years ago (Tacon, 2016). Some datings are as early as 10,000 years ago, perhaps driven more by nationalistic fervour than science. There don't appear to be any good grounds for assuming that skis and skiing first appeared in this area.

Allen (2007) gives a good modern review of the early evidence for skis and skiing, in the first chapter.

Alas, the Rødøy skier was seriously damaged a few years ago by a "restoration": https://www.smithsonianmag.com/smart-news/norwegian-youth-destroys-one-earliest-images-skiing-trying-improve-it-180960013/

References

Allen, E. John B., The Culture and Sport of Skiing: From Antiquity to World War ll, University of Massachusetts Press, 2007.

Dresbeck, L., "The Ski: Its History and Historiography", Technology and Culture 8(4) 467-479 (1967). https://doi.org/10.2307/3102114

Kolpakov, E. M., "Economic activities in the petroglyphs of fennoscandia", Quaternary International 541, 63-73 (2020). https://doi.org/10.1016/j.quaint.2019.10.011

Tacon, Paul SC; Huisheng, Tang and Aubert, Maxime, "Naturalistic animals and hand stencils in the rock art of Xinjiang Uyghur autonomous region, Northwest China", Rock Art Research: The Journal of the Australian Rock Art Research Association (AURA) 33(1) 19-31 (2016). https://search.informit.com.au/documentSummary;dn=050400631479028;res=IELAPA