Are omens always bad it seems from the examples that you give that something bad often happens following an omen. Boudicca seems to fit within this idea too as things did not go well for the Britons in spite of Boudicca’s supplications
I don’t think omens have to be bad, however, the word has come to have a usually negative meaning, hence too the word ominous. Boudicca, according to Cassius Dio, used the hare to determine whether or not the gods were in favour of a British victory – according to the hare’s course, it was supposed to be auspicious. Unfortunately for the Britons, it didn’t quite work out that way despite their having believed that the gods were in favour.