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I am considering taking a few skiing lessons soon (never skied before), and the amount of specialized gear seems to be a lot. I hike a bit, and have good merino socks, which are great for warmth as well as dryness, and go well with hiking boots. However, all ski socks seem to be knee high.
Does someone know if I can make do with the calf-length socks in downhill skiing boots for the duration of the lessons, or if it is strongly recommended that I get a pair of specific ski socks instead?
You most definitely do not need specialized socks. If your socks suit you when hiking, chances are good they will for skiing as well. And as you said merino should also be good for warmth.
As for the length: The important thing is, that the upper end is outside/above the ski boot. If the end is inside, that's a point of friction and especially on your shins, that's problematic. So if your calf length socks go to just below the knees, that's fine - best to test with the skiing boots.
Some walking socks have different grades of wool and/or different construction around the foot compared to around the shin and calf. A ski boot will (or should) fit close around the shin and calf. A sock that is rough can rub the shin until it bleeds. (I have seen the effect. An able, but not good, skier skied too far on his first day. He rubbed his shin raw. He could not ski for the rest of his one-week holiday.) Think about you normal blister prevention rules, avoid having rough material rubbing your skin. You want the sock to stick to the skin and any rubbing to happen between sock and boot.
I recommend skiing socks, although I expect that some other types of sock would be suitable.