New Englander and biologist here! This is all correct and EXTREMELY important.
The biggest thing to understand here is that this isn't, "Oh, you can die from exercise if you're out of shape!"
This is, "You can die from strenuous exercise in the cold, regardless of your physical fitness."
Your circulatory system is a major, major part of how your body maintains a regular body temperature. When it's really hot out, blood vessels dilate (widen), which thins the walls a bit and makes it easier for heat to escape the blood stream. This is why when you are really hot (it's hot outside, or you just finished a work out at the gym), you get flushed. The red color of your skin is from dilating blood vessels.
In contrast, to conserve heat in the cold, your blood vessels constrict. When they get narrower, the walls are thicker, and heat can't escape as well.
But the problem is that when blood vessels narrow, it increases your blood pressure. A lot. And if you are not in peak cardiovascular shape, this can be a huge risk for your heart if you then do a lot of strenuous exercise, which shoveling absolutely is. When I was going to the gym regularly, it was still tough.
Tips to decrease your chances of dying from shoveling:
Try not to lift snow when you shovel. It's better to push it to the side whenever you can, and if you do have to lift it, that's okay, but don't dramatically toss it over your shoulder. Just kind of lift it off the ground and dump it aside. Keep everything low to the ground.
Bundle up. The warmer you can keep your body using insulation, the less your blood vessels will have to constrict. This is especially important for your core, but also your arms and legs.
Consider compression socks, if you have any, to keep your blood flowing easily in your lower legs.
As mentioned above, do an actual exercise warm-up before you shovel. Again, it's not that shoveling is an Olympic sport, it's that you are about to put a huge strain on your cardiovascular system and you need to prepare.
Take frequently breaks inside. This is probably the most important one, and the one that a lot of people are the worst at. Don't power through to finish it all in one go. Set a loud timer on your phone and take lots and lots of breaks. Take those breaks inside where it's warm. Because again, the issue isn't just the activity, but the temperature.
Finally, and I can't stress this enough: NOT shoveling is not laziness, and if you can avoid doing it while still clearing your walkways, steps, or driveway, you should. This could mean using a snow blower if you can get your hands on one, but it could also mean hiring someone or using a lot of ice melt. Ice melt isn't ideal because it doesn't really clear snow, but it's better than nothing, will help prevent slipping accidents if you use it consistently, it's easy to apply, and you can get pet-safe versions.
Hiring someone isn't a sign of laziness or a privileged attempt to avoid a chore that we all should have to live with. Hire someone with better cardiovascular fitness! Hire someone who owns proper winter gear! Hire someone who is well-practiced in shoveling so they don't overtax themselves! Hire someone who owns a snow blower! Again, I live in New England, so your mileage may vary, but our town's facebook page is littered with high schoolers and their parents leaving phone numbers and neighborhoods and cost estimates. Others are offering it for free for elderly and disabled neighbors. This isn't like hiring a house cleaner or a landscaper.
When it comes to clearing snow, we really do need to do it, since otherwise sidewalks become impassable or dangerously icy. But anyone who complains that, "Oh, people are so LAZY about it!" needs to stop, and everyone needs to remember and understand that clearing snow in the cold is extremely dangerous, and we have to take care of our circulatory system when we do it.
