"Biting" means more to me than "cold." It is certainly a more vivid description, establishing what a person would feel. You could argue that there is some redundancy, but I find the phrase idiomatic and, in fact, euphonious.
If you mean tautology as in rhetoric, that biting is a restatement of cold, then I would say no.. Biting is soemthing that causes a stinging sensation.. It is not necessarily the case that a biting wind is a cold one. A warm wind carrying sand or salt can be irritating and biting..
cold, biting is fine.. it discusses 2 aspects of the wind and neither unit facet displaces the other