Welcome! There is less oxygen in the air at high altitudes, which can cause stress hormones to be released, which is hard on the heart. Generally if your heart problem is under control, you will be okay. People with undetected heart problems are more likely to have issues, probably because they don't know what to look for. There are a few articles on the web about sudden death in tourists caused by undetected heart problems, but I think that is pretty rare. If you experience palpitations, shortness of breath, or other symptoms, sit down and rest. If that doesn't work, find a doctor.
I experienced altitude sickness every time I went to Colorado or New Mexico to ski. Since I come from a very low altitude (50), it could just be normal altitude sickness. It never happened while I was actually skiing, but rather while I was waiting in a lift line or in the slope restaurant, and seemed to be related to getting overheated, although that could just be a symptom. I would get light headed, short of breath, and feel like I was going to faint. The first time it caught me off guard and I actually "passed out" but came to within seconds. After that, I expected it and if I felt the symptoms, I took off my coat, sat down, and put my head down. I also know now to not go skiing the first day so my body has a chance to get used to it.
Make sure you take it slow for the first few days and you should be fine.