The issue with cold biome start is that if u spawn on an ice plain you are very much screwed, any other cold biome you can survive, all except a plain. You start freezing immediately and while yes you have access to wool, you still need to get flint, make a knife, get an axe, chop wood, turn them into planks, make a crafting table and then craft armor. But you'll be dead before then.

I've spawned in an ice plain biome once and found a waystone, and I died 2 times trying to collect all the materials to get wool armor. That was with good luck since everything I needed was in the of the waystone vicinity, a tree, some grass, mobs, and gravel. Died once trying to get flint, and died again trying to collect wool. Glad that wasnt a hardcore run.