Thank you everybody for your comments. There are a few things that can be clarified thanks to these comments.
It looks like there are 3 different stats that combine to give your total number of completed races. There's the one on the General tab, the 2nd on Online and the 3rd on Blizzard Mountain.
Additionally it seems as if this achievement is tracking all your completed races plus the number of snowmen smashed. So if you add the 3 different race stats and the number of snowmen it should come to roughly what the achievement tracker % shows.
While grinding the Bucket List #4 it sounds like the quicker way is to get 19/20 and then restart the challenge, skipping all the reward screens that you have to sit through if you complete the challenge. Every 19 snowmen smashed should raise the achievement tracker by 2-3%.
Once again thanks to everybody who commented with these points.
Ok so obviously there are 2 different requirements for this achievement and it's on you which one you decide to go for.
If you've previously met either of them then the achievement will pop immediately when you load up the game.
And if you've already unlocked the full 2500G before this update and have been keeping up with the challenges then chances are you're pretty close to having done 1000 races. You can check by going into the menu, scrolling across to the Progress tab and selecting Stats. Then in the top right corner of the General stats you'll see Number Of Races. I can't confirm that this is the number used for these 4 title update achievements but it seems pretty likely.
However doing the races, as with all 4 of these title update achievements, will be much slower than doing the skills.
The easier and quicker way to pop this specific achievement will be going for the 1000 Snowman skills. Again you can check by going to the Progress tab, selecting Stats and then Blizzard Mountain. Down near the bottom of this page is the number of snowmen you've smashed. In my case after doing all the Blizzard Mountain DLC I only had about 60 of these so this is where the grind begins.
From what I can see the quickest way to smash snowmen is to load up the Blizzard Mountain Bucket List #4 challenge which requires you to smash 20 snowmen in 2 minutes or less. This challenge sticks way more snowmen around Whitestone Village than there are in Freeroam mode and they all respawn each time you start the challenge. So run the challenge and immediately restart to do it over and over. Even after only doing it a couple of times I can get the 20 snowmen in about 90 seconds which if you add loading times works out to probably around 2 minutes per run which even if you're starting this from 0 should net you the achievement in roughly 100 minutes. Not nearly as bad as you might have originally thought.