Threaten, menace both mean to announce or forecast (as by word or look) an impending or probable infliction (as an evil or an injury).
Threaten basically implies an attempt to dissuade or influence by promising punishment or the infliction of reprisals upon those who disobey an injunction or perform acts objectionable to the speaker.
However the term has been so extended in its meaning that it is often used with reference to things (as events, conditions, or symptoms) which presage or otherwise indicate something, and typically something dire or disturbing, to be about to or likely to happen.
Menace is a somewhat more literary term than threaten , and it carries a much weaker implication of an attempt to dissuade or influence and a much stronger suggestion of an alarming or a definitely hostile character or aspect.