No, it doesn't, which is why the English is "It is cold this morning." :P Did "has" come up in a multi-choice or something?

I'm guessing that was not an alternative that the course maintainers had added, but one made up by Duolingo's automatic expansion/contraction of things such as "it's"... in this case incorrectly expanding "it's" to "it has" (as in "it's taken me two weeks = it has taken me two weeks").