I often do a morning workout so I have two breakfasts; a really small one so that I'm not running on a completely empty stomach (or swimming...2 mornings a week I swim), and then eat again about an hour after the workout. I do about an hour each time, though. If you're going out for less than 30 minutes, I wouldn't worry about eating unless you feel you want to. I go with like a small granola bar (100-150 cals), sometimes a small bowl of cereal, and coffee.
You might want to drink a little before, at least.
As for burning muscle, we actually often DO burn muscle as we work out, but it's not a substantial amount. Some studies have shown, in fact, that your actual fat burn is a little bit higher if you work out in the morning before you eat. The reason is, when you wake up your glycogen stores are low. Your body uses glycogen for fuel, and it's stored in your liver and your muscles. When your body has food it converts that to glucose for fuel (simplified version of what really happens), then goes to your glycogen stores, then to fat stores. It's never going to burn ALL FAT or ALL MUSCLE.
blockquote3. The oxidative metabolism of carbohydrate and lipid supplies most, if not all, of the ATP during prolonged submaximal exercise. Muscle glycogen, blood glucose and FFA are the key fuels. The relative importance of the various substrates for exercise metabolism is primarily determined by exercise intensity and duration, although training status, dietary manipulation and environmental factors can modify the metabolic response to exercise.blockquote
This is from a study done in 2000, which pretty much sums of up what happens during a longer workout. During a longer workout, most of the "fuel" comes from blood glucose and free fatty acids. That's why when you get into higher duration workouts, you need to fuel during them. Your body can, and does, convert fat (usually the FFAs floating about which do come from adipose) to glucose but it is not very efficient at doing that and that can cause a "bonk." (Bonk=out of fuel, feeling bad, icky, nasty moment. Do Not Want.)
So in short...if you're doing a short workout, no you don't need to eat before unless you feel better when you do. If you up your intensity, you may find you CAN'T eat before. (I have almost revisited my corn flakes on hill workouts in the morning a few times.) If you're going longer, yes you need to top off your fuel (you use a lot of glycogen while you sleep). Either way, you need to hydrate. YOu may not need to take water on a cool morning if the run isn't any more than 3 miles, but you should drink some beforehand.