We fix New Year's Day by moving it to March 1st. Simples!
This means the year starts when the weather is getting better and the flowers are coming out.
This means we've fully recovered from Christmas when we go to our New Year's Eve party (at the end of Feb).
This means leap days will be the last day of the year.
Let's say we make this change in 2030 as shown ...
New Year's Day is March 1st. (i.e. 1-1-2030).
The last day of the year is February 28th or, if it's a leap year, February 29th. So every leap day will now be New Year's Eve.
Since we're messing with things, let's correct a major injustice. Monthly paid workers have, until now, been expected to work an extra day for free, every leap year. Well - no more! Since Feb 29th is now New Year's Eve, let's designate it a holiday.
One minor problem is that 2029 will need to be 14 months long as shown ...
Do we still party at the end of Dec, 2029 and get the next day as a holiday? Hell yes ... for one last time. And we get to do it all again on the last day of Late-Feb, 2029 and Mar 1, 2030 (i.e. the new New Year's Day).
But the good news doesn't stop there. Some lucky people will get a year younger! Let's say your birthday is Feb 15th. As a one-off side-effect of this change there are 24 months between Feb 15, 2029 and Feb 15, 2030. You're welcome!