More exactly, months were March, April, May, June, Quintile, Sextile, September, October, November, December, January, February and, sometime, Mercedony, in that order: years started with spring, at the Ides of March.
As far as I know, January and February were added after December, not before March. The New Year day formally moved from Ides of March to Calends of January with the Julian Calendar, but it wasn't much respected before the Gregorian Calendar definitively generalised the beginning of the year with the alleged anniversary of the circumcision of Jesus, the 1st of January. Equinox of Spring was a much more appealing New Year Day than the approximative perihelion.