For drag racing, if you need to cool, use ice. That's what the drag racers do. For Pike's Peak, ice -- that's what Brandon does. For longer-term racing, you'll need to go to water cooling or engineer a very good flow of air over the motor. There's nothing wrong with air cooling; if you think about it, the radiator on a water-cooled system is just another way of dumping the heat to the air. A radiator just allows you to put the cooling where you want it and maybe offers more surface area.
When I was at General Dynamics, we were working on infrared detectors which needed to be very cold; we used a cryostat using expanding CO2 just as you describe. But the bottle was heavy, it was dangerous (as any highly pressurized bottle is), and it lasted maybe a full minute. The calories of heat you can absorb that way just aren't worth it.
Someone once suggested slowly spraying (misting, really) water on the motor, which might work. Water absorbs a ton of heat as it evaporates. I'd worry about the motor being totally watertight, especially the bearings, but it might be okay.