A practical question for participants on the Elbrus programmes is whether existing ski kit will do: can I just bring my ski clothing? The short answer is yes, with caveats that are worth understanding before you find them out at 4,000 m.
Insulation
Ski jackets and trousers are usually insulated, and often insulated differently from each other. Mountaineering shells generally are not. That sounds like an advantage for the ski kit until the first acclimatisation walk, when you are on grass at 20 degrees and your only shell is a three-layer insulated jacket. The same problem appears in reverse on the descent from the summit, which can be hot in the sun and unpleasantly cold in the wind within the same hour.
Ventilation and breathability
Ski clothing is often heavier or less ventable than a climbing shell, because it is designed for a sport with a different work rate, though this varies a great deal between garments. Skiing alternates effort with lift rides; climbing Elbrus is continuous output for hours. If your layers get damp from the inside, their insulating value drops sharply, and it is entirely possible to be cold in the warmest clothing you own.
Weight
Weight is irrelevant on skis and it is not irrelevant when you are carrying it uphill. A ski setup can be materially heavier than a climbing setup, which compounds across a week.
What this means in practice
Ski clothing works on Elbrus if you manage it deliberately: avoid overheating even slightly, and build your layers so you can shed insulation rather than being locked into it. An uninsulated shell is a common layering choice for exactly these reasons, because it lets you add and remove insulation independently. What any given programme expects you to carry is set out on its own equipment list.
If you would rather not buy at all, gear rental covers what can be hired for the trip. For preparation rather than equipment, see training guidance. Skiers looking for a ski objective rather than a walking ascent should start from ski touring.