Additionally, machinery like this is usually designed to run at a certain temperature which is usually above ambient. Everything expands slightly as it heats up, and at the designed running temperature all the designed tolerances are correct. So if you cool it to -40C, you're going to shrink everything and potentially cause more problems. What would probably be more beneficial to the performance and life of a spindle would be to know what the operating temperature was supposed to be (obviously we don't have this kind of info for the cheap Chinese spindles) and then control the temp of the coolant to maintain the spindle at that temperature.
CNC mill build thread: http://www.cnczone.com/forums/vertical_mill_lathe_project_log/110305-gantry_mill.html