Weather-wise, it is easier to start well ahead of winter. That gives you time to learn the road and learn your truck before winter challenges rise. Still, it is not that big of a deal. You can learn the road and learn your truck in the winter too. If it makes job sense for you to start in January, do so.
Money-wise, whatever month you enter the business, be sure to have a financial cushion (money in the bank) to sustain you through slow periods, unanticipated breakdowns, unplanned trips home, periods of illness, etc. Your financial cushion will be more of a factor in your success than the weather.