I do it all the time. My wife and I work out together in the morning from 5:30 - 6:30 and we haven't had any problems. Make sure you drink a couple of glasses of water to get those body processes moving and make sure you have a clean diet the rest of the day. Eat a good high protein meal soon after your workout to refuel your body and let those muscles start rebuilding, then keep up your eating throughout the day. Your last meal of the day should provide all the nutrition you need to get through a workout the next morning.
Cardio days work a bit different. After a hard cardio workout you want your system to feed off of itself. If you can, wait at least an hour before eating for max fat burn. Its worked for us for 14 months now.
B-Mac