I think it's supposed to be an answer to a question like "When are you going?", but the I personally would include say "ym mis Ionawr" (in January) instead.
Further into the course you are taught to say ”ddydd Iau” for ”on Thursday” with a mutation. Could one not mutate ”mis” to ”fis” to mean ”in January”?
No because in January would be "ym mis Ionawr". Yn when it means in causes a nasal mutation and "M" doesn't mutate nasally.