King #NumaPompilius is said to have recognised that this was silly and introduced two new months to cover the winter period, Ianuarius and Februarius.
Now, the Romans didn't think of dates the same way we do today (or really as other people in the ancient world did, because the Romans were the worst at timekeeping). They thought of each month as having its kalends on the first day, its nones on the 5th or 7th, and its ides on the 13th or 15th, and all dates were given relative to those.