Thanks for mentioning ‘false friends’. I’d never heard the term/concept before.
Grippe isn’t that archaic. In “Catcher In The Rye” Holden says that his sister feels “grippy.”
In modern Mandarin the most common word for it 感冒, just means a kind of transmitted infection.
However, on checking my dictionary, there are other, probably older words, like 风寒, which refer to both the wind and cold weather.
Grippe is the French for flu, as distinct from a cold (though I have known French people convinced that the slightest draught of cold air will bring it on - but then again, in America, disappointments in love will do it - Adelaide's Lament {Guys & Dolls ~ Broadway, 2009} - Lauren Graham - YouTube )
The false friend of constipation is interesting, considering the propensity in Spain (and often in France for that matter) for medicines to be delivered by suppository (even for conditions sited up the other end of the body).
There is a relationship between cold weather and the prevalence of the common cold, but it is not a direct one. Being out in cold weather doesn’t bring on a cold. However, the fact that people spend more time indoors in close contact with others when the weather is cold provides better conditions for colds to be transmitted.
It appears so far that the linguistic relationship between cold temperature and the common cold is confined to areas that experience a cold winter (although the relationship is not universal).
In poking around, I was surprised that in English the sense of cold to refer to the common cold only goes back to 1770.
My favorite in Spanish is embarazado/a, which does not mean embarrassed but pregnant. If you inadvertently tell someone you are embarazada when you are embarrassed, you might well end up the latter. 
Well it’s better to just say there is some correlation between cold weather and incidence of the cold virus.
Whether that’s because people spend more time indoors is debateable; other hypotheses are available and it may be a combination of several factors.
Furthermore, there is an overlap between some of the symptoms of just being very cold and the common cold. If you go out on the first really cold day of Autumn in a t-shirt you may well find you have a runny nose and sore throat later. It’s not a real cold (virus) and the symptoms will disappear quickly, but still it’s another reason why many cultures have this association.
Lest I seem like I didn’t say “thanks,” I just wanted to, well, thank everyone for the contributions. This is really interesting and it seems that while nowhere near universal, the idea of “cold” as a term for the common cold is very common.
This is what makes the dope great- such a range of knowledge and experiences.
In the parts of Mexico I’ve lived, gripa is much more common (for a regular cold, not just flu), though resfriado is understood.
In my arabic, the first word for cold (sick) I would normally use is berd, which is exactly cold.
My WAG: People coming down with a cold often feel chills. I guess they are shivering as a way of raising their temperature. I further guess that they associate those chills with the ensuing cold and that is why they believe that getting chilly causes which repeated research shows it doesn’t.
I thought of that as well. But fever is an uncommon symptom of the common cold in adults. Instead, a high fever is a symptom of the flu, which used to be called the grippe. And colds and fever have been distinguished for a long time, as in the adage “Feed a cold and starve a fever” (which however has no truth to it).
The most common Korean word for the minor disease ‘cold’, ‘gamgi’ (감기/感氣) is a Sino-Korean word coined in Korea, hence only half the same as the most common modern Chinese word (感冒), nor the same as any modern Korean word for cold temperature. But, the etymology of both is actually arguably related to cold temperature, since 感 could mean ‘affected by wind or cold’ in old Chinese medicine. However, the connotation of the same character in 感染, a word shared by both modern languages meaning ‘contagion’, is ‘spreading disease’. The most common meaning of that character is ‘feeling’, which makes the Sino-Korean word seem arbitrary if one assumes that meaning in ‘gamgi’. 氣 is air or breath in this case.
The less commonly used indigenous Korean word for (disease) cold, ‘gobbul’ (고뿔)’, has no connection to temperature: ‘go’ as in ‘nose’ (now spelled 코 as a standalone word), ‘bbul’ as in (an animal’s) horn.
What propensity? Last time I even saw a supository was over 15 years ago, and I’ve got a mother whose bathroom contains so many drugs it’s probably illegal. Suppositories are sometimes available as an alternative to oral meds for patients who have trouble with orals, but they’re a really uncommon delivery method.
Faroese has krím, with some cognates, like krimmen, in northern Swedish dialects.
Actually, I don´t find the connection common cold / cold weather difficult to understand. My nose (and eyes!) are more or less constantly runny whenever i am outdoors in wintertime!
Wiktionary, being a multilingual, hyperlinked dictionary, is pretty good for researching these kinds of questions. If you look up the English word “cold” and examine the section on translations, you’ll see the equivalent term in dozens of other languages. For many of these, you can click through to read the entry; if the word means or comes from that language’s word for “cold” then this may be obvious from the etymology, related terms, or (English-language) definition that Wiktionary gives.
For example, you can see that the Greek word for a cold is κρύωμα, and the entry for that word shows that the word is related to κρύος, which means “cold” in the sense of temperature. By contrast, the Greenlandic word for a cold is given as nuak, whose only other meaning is “spit, saliva”, so it’s probably not related to the Greenlandic word for cold temperature.
Tagalog is one language where the words are unrelated. The illness is sipón which can also mean the mucus / nasal discharge that goes with a cold. Cold temperature is kalamigán or kaginawan; these are noun forms, with adjective forms malamig and maginaw.
In Thai, หวัด (/wat/) is the word for the common cold. Another word, หวัด, spelled and pronounced identically is a verb meaning to scribble. (My informants are unaware of any etymological connection between these two words.)
Scandinavian is similar verb forkjølt/förkyld - noun forkjølelse/förkylning
It’s the only infection that has its own verb in these languages, at least that I can come up with right now.
It’s like if English had “I’ve been encooled” or “I’ve gotten an encoolening”, it’s clear that the root is getting cold, but it’s not the same words used for actually freezing.
Russian has простуда for the common ailment and холод for the general temperature/sensation (with the corresponding verb простудиться and adjective холодный respectively). Google Translate, however, tells me that простуда can also mean ‘cooling that an organism has undergone’, so the whole idea of the chills being a sign (or popularly assumed cause) of impending illness seems to be there.
“Простуда” is derived from “стужа” which means “freezing cold”