Some brushless motors have the windings come out the wires. You will basically turn the motor into a paperweight if you cut the wires on that type of motor too much.
Depends on the motor. One like a neu which only has short wires coming from the motor must'nt have them trimmed as they are actually extensions of the windings from within the motor- solder on extensions or use bullets & extension to reach the esc. Cutting them down will soldering them very difficult as they are coated with epoxy as they enter/exit the can.
A motor like the castleneu can have its wires trimmed as they are only that long for convenience's sake (make them long enough for everyone and let them trim as required). I wouldnt cut them down too much though incase you want to use the setup in a different vehicle in the future- leave at least a couple inches from the motor.
Wont make it run slower, its more a case of the windings being coated as they enter the motor, so if you trim off too much you would have difficulty soldering to whats left of them afterwards (as stated previously).
To reiterate what has already been said by suicideneil. It is okay, and actually recommended to shorten the length of wires on the Castle Neu motors and our 36mm motors. The regular Neu's should never be cut.
The rule of thumb that I follow is if the wires are limp and like wet noodles, they are simply extensions of the motors internal wiring, so you can cut 'em; if they're stiff and hold a bend, they are part of the internal wiring, don't cut e'm.
Shortening the wires on the right motor has positive effects; it makes for a cleaner install, reduces radio interference and improves signaling between the speed control and motor.
Shortening the wires on the wrong motor can cause issues with timing, and as stated already is difficult to solder on because they have a coating that makes soldering near impossible. FYI: acetate helps remove this coating if you find yourself in a situation where you need to solder on coated wires.
Hope this helps some. If you have any questions don't hesitate to ask!