Milk was designed by nature for infant mammals only. We humans liked it so much that we figured out how to keep on drinking it after we were weaned.
Cold foods aren't thought to cause cancer. I mean seriously, how would that be harmful. Eating lots of sugar and junk food isn't healthy but again, not a direct cause of cancer. Eating fruits and vegetables and healthy foods in general reduces the risk of many diseases including cancer, but notice the words risk reduction - it's not quite the same as preventing cancer even though many people use these expressions interchangeably. People with exquisitely perfect diets can still get cancer and people with terrible diets can live to a ripe old age without getting it, but one group has a lower rate than the other. Ditto for heart disease and a whole bunch of other health problems.
This map shows the cancer death rate by country:

As you can see, China has a significantly higher death rate than we do. But we have a higher incidence rate, so obviously we have a more successful treatment program than they do:

But since cancer risk is directly related to age, you also have to take life expectancy into account. We're at the top of the chart for both life expectancy and cancer rates, so nothing terribly out of line seems to be going on. China doesn't look significantly better than us when you consider how much shorter their life expectancy is.

Some of these countries obviously have some errors in their reporting. I mean seriously, Libya has a high life expectancy and a low cancer rate? That doesn't make any sense at all.