For example, my dad, when he feels ill, always uses the phrase "I'm under the weather... Uff"
But the origins of the term is not related to cold weather at all. In fact, "under the weather" is a saying with a nautical background. Sailors and passengers on ships would get ill or seasick during their journey. Sick passengers were ordered to go below deck, which was believed to be the most stable part of the ship as well as a shelter from the weather. This was to ensure a speedy recovery from whatever was ailing them.
So, it’s no matter what profession you have, you use this phrase as a synonym for being ill. But it means also "being intoxicated" :D