Researchers at North Carolina State University have actually calculated that, in order to visit the house of every child on Earth, Santa Claus would have to travel a total distance of 122 million miles (about 196 million kilometres) - see Wise A, “FYI: How Long Would It Take Santa To Deliver Presents To Every Kid On Earth?” (Popsci.com, 2012).
Assuming that he drove a medium-sized petrol car (a new Volkswagen Golf 1.5, for example), which produces an average of 120 grams of CO2 for every kilometre travelled, he would produce a total of almost 24,000 tons of CO2. See “Car CO2 and Fuel Economy Figures for Volkswagen Golf Vehicles - Page 2” (Fleetnews.co.uk, 2019).
To put this into perspective, “Trees of Strength” (Ncsu.edu, 2019) states that one tree can absorb up to 48 pounds (around 22 kg) of CO2 per year. At this rate, the same tree would take over 1 million years (or a million trees will take one year) to remove all of this CO2 from the atmosphere! In contrast, a medium-sized hybrid car might produce around 45g/km and so 8820 tons of CO2 for the same journey.
Also worth looking at “Car Fuel and CO2 Emissions Data” (GOV.UK, 2012).