I was told that wool will make you worm even if it is wet!
What do you think about that?

They keep you "partly" warm, but it's still uncomfortable. The problem is when riding, the wind will go thru the fabric and you'll have next to zero benefit from the insulation. Insulation works by trapping a layer of dead air (still, not moving) around you. If the wind takes that air away, you feel colder. That's why it's colder on a windy day. And on a bike, it's always windy.

Try searching this forum as well as the winter and commuting forums for "waterproof socks".

I've a few pairs of merino wool socks. Ideal for winter are the merino wool lined Sealskinz waterproof socks.

Also Groundeffect (www.groundeffect.co.nz) do several different weights of merino wool socks which are all good.