There are all kinds of alternatives/choices in
base layers and the very best will be made of or blends of hydrophilic polyester, acrylic and -- yes -- Merino wool.
On edit: You should understand that these fabrics -- Merino included -- have very good hydrophillic properties, meaning that they transport perspiration away from the skin, unlike, say, cotton which holds it next to you.
Having said that, it's body heat that drives the dampness through the garment, to an outer layer. So layering is the key ... and if you overheat, then stop moving, no piece of clothing will entirely solve the issue.
Proper clothing + brains and experience is the total key to safe and comfortable cold-weather sports.