It's common to see different lists of weather-related deaths and injuries. It is actually a very difficult question to answer.

For one thing, there isn't much good data out there. Weather is not usually noted on death certificates or medical records at all. How you define "weather-related" also plays a big role. For example, weather can affect people after the actual weather event is over--does that still count? I read a research paper one time that showed that the effect of unusual cold often continues for days after the temperature has normalized, while the risk from unusual heat tends to decrease as soon as the temperature drops.

And who is asking the question makes a big difference, too. Someone in public health versus a meteorologist vs someone in the insurance industry vs emergency response policy wonks will tend to come up with different lists because of their differing priorities and biases.

Until we have a better data gathering system, I suspect that a lot/most of the advice that we are given is based more on anecdotal accounts of specific people or specific events, and based less on these broad, overall views of weather-related data. E.g. it's common to hear the advice to NOT seek shelter in a freeway overpass nowadays based solely on this one famous video. There may still be people recommending that folks do this when a tornado is approaching even now.