Switching 30 watts of LED about 2000 times a second -- is a TO-220 MOSFET okay?

but I was worried about them burning up during switching.

Switching dosn't dissipate any more heat if you do it fast, it is when it is slow you have the problem. That is not to say how often per second it switches, it is the time it takes the FET to go from on to off.
This is a function of the drive circuit into the FET. If you connect a FET directly the use a 100R resister in seriese with the gate to keep the current down to safe levels for the arduino.