Racing again after a crash


I like your horse riding comparison. In motorcycle riding, you look where you want to go by turning your head. If you turn your head into the turn, the body and bike will follow. The worst thing you can do is lean upwards and look straight. The other part of turning is leaning the closest handlebar into the turn, not turning the handlebar. This places you on the side of the tire (yes- you are supposed to ride there). This is why bike tires are rounded and car tires are flat.
Practice turning your head and leaning the inside handlebar into the turn and keep doing it until it feels natural. You will learn to keep your speed in the turns this way. Even if you do slide and fall, a low side fall under the bike is always less damaging to your body and bike than a high side fall.