The vow would normally be uttered on the 1st of January (OCD 3 s.v. votum), but notice that the (rather old) commentary on the quote below state that it was to eb done on December 30th.
The emperor Trajanus.
"To the emperor Trajan
We have acquitted, Sir, and renewed our annual vows for your
prosperity, in which that of the empire is essentially involved,
imploring the gods to grant us ever thus to pay and thus to repeat
"Trajan to Pliny
I received the satisfaction, my dearest Secundus, of being
informed by your letter that you, together with the people under
your government, have both discharged and renewed your vows to
the immortal gods for my health and happiness."
Pliny the elder - epistulae X 35 & 36
Translated by William Melmoth