The Model X cooling system would intuitively be larger than the 5.5 kw capacity of the Model S. Tesla has known for a long time that the Model S rear kids seats overheat the kids in the sun as there is no real air back there.
Bigger vehicle, more occupants, more interior space, bigger battery capacity => bigger Heating & Cooling Unit.
How much bigger, good question. Perhaps the response to the question also matches the service center adjustment to my model S HVAC almost 2 years ago, when I complained of insufficient air flow, I got back "no trouble found" and a fan speed that goes to "11" as opposed to "8" like before, or newer loaner cars. It is really quite loud on recirculate, but does the job quickly.
The HVAC unit is a 400 VDC heat pump compressor custom made by Tesla, that works with the front mounted radiators, in a 3 zone (Model S) configuration (battery, driver/front passenger temp zones). It could be 4 zones if indeed it also directly cools the motor, but I have not investigated that far. Tesla doesn't have a rotating drive shaft on an ICE to connect a traditional car air conditioner, so they had to build their own. Most likely the zones are simply a combo of flow restricting valves, and total coolant flow through a multi-loop system. 5 gpm of fluid at 30 degree temp differential has more capacity than 3 gpm fluid, but takes more energy to push through the same hose.
A 3 row Model X would presumably have front / rear controls, so that is at least one more zone than the Model S.
Ludicrous mode could also push a requirement for cooling both front and rear motors, as well as more battery cooling capacity.
If the Tesla compressor is anything like the variable speed HVAC unit I have at home, it can draw very low power at lower speeds, and then ramp up to "full power" which gets noticeably louder, and eventually efficiency drops. 8 or even 12 kw will do wonders for comfort, but at some point the range crashes. Early Model S software included "Range Mode" which limited HVAC performance to increase range, substituting seat heat for air heat.
Thus the real size in the founders edition cars could indeed be 10 kw capacity, but software limited to 7.5 to 8.5 kw range. Unless my intuitive guess of what they should have done is more optimistic than what they really did, in which case, DOLT!
Mark.