I found this study, reported by WemMD, very encouraging for people who have heart problems. Basically, it states that:

“People with heart failure can regain 70% of their exercise capacity if they stick to an exercise program,” says Axel Linke, MD, an assistant professor of medicine at the University of Leipzig in Germany. Linke worked on both studies.

70% is a big number and that heart disease doesn’t have to be the end of activities you enjoy.