i have a 2003 mdx and it only happens when the car is cold or in cold weather.

When I turn it on, it would make a rough choking noise (like the sound you here when you turn the ignition when the car is already on) but then it quickly goes away and I'm left with high pitch humming / squealing noise that eventually fades away.
What weird is sometimes when I move the gear from Park to Drive, the rpm drops and the engine dies and I just have to it turn it on again.

Any ideas?
this only happens when its cold / in the morning after overnight

 

I'd check your throttle body because it might be dirty. Then check the PS for that whine. Could also be a bad torque converter.

 

Does it sound like belt whine? Try spraying some wd40 on the belts in front. If it goes away, then you should replace the accessory belt and pulley.