Well, gospozha Julia,
This can get a little complicated, for a variety of reasons. And I'll give you a little background and some thoughts directly. But first, what you are talking about falls into two, somewhat overlapping subdisciplines, practioners of which sometimes read and talk to each other and sometimes dont.
The first is Semantics. What you are talking about falls within the general discussions in Semantics on connotation and denonation. The first has to do with meaning or reference in the narrow sense of a "word", i.e. a lexical item. So 'sheep' refers to various members of the genus Ovis. That's denotation. But talk about sheep among devout Christians and you get one set of emotive "pictures" and recollections and associations; talk about them among pastoralists and you get another, albeit overlapping set, but talk about sheep among Scottish Highlanders in the 1800s and you get a quite different set of associations. This is connotation. There is a fiar amount of literature discussing these things, so do your search among Semantics as a general category and connotation, or connotive meaning, or "associative" or "emotive" meaning.
Now, a waning. These terms also have a long time use in philosophy. Sometimes you see the German terms Sinn and Bedeutung. BUT -- the use in philosophy is somewhat different. Im not saying not to read the philosophers, but rather to be wide awake and watch for these differences in focal direction of usage.
Sometimes these kinds of differenc es lie purely in geographic and climatological variation. June to a New Zealander in Ivercargill (at the tip of South Island) has one set of associations, but to a North American or a Russian, a quite different set. This has little to do with culture and a great deal to do with the obliquity of the ecliptic. So that's of no linguistic interest. Or cultural. But Easterto a North American Protestant will evoke one set of associations and "fond" or not so fond memories while Pascha to a Russian Orthodox Christian will evoke a rather different, though overlapping at the core, set. That is of cultural interest, though actually rather obvious and linguistically rather trivial. That is to say, it is a difference that is not a function of language at all but rather a function of clear differences between growing up in Serbia, Bulgaria, Alaska, or another predominantly Orthodox culture versus growing up in a predominantly Protestant Reformist culture. It's not culturally trivial but it is linguistically trivial. And it is of very little interest to linguists. If it has anything al all to do with "mentality" or "way of thinking", it is strictly a derivative of the cultural differences -- certainly not a cause of them.
A more teasing type of associative difference that does come on at least the borderline with linguistics is the kind wherein two languages will have two different words for the same thing but the differences derive from two different systems of semanitc range. Whether your "new potatoes versus "young potatoes" falls into this group I dont know -- I doubt it. But an example of one that probably does is these two from English and Welsh:
'brown sugar' in English but
'red sugar' in Welsh.
That is, Welsh is siwgar coch and the word coch is the same word that is used for the National Emblem of Wales that appears on the Flag -- Y DDraig Goch ''The Red Dragon.' The dragon is bright deep red, but the color of "red sugar" is the same in Wales as everywhere else, "brown", i.e. a dull, reddish brown, not ever very russety russet. I.e. the same absolute color difference between the "red" of the dragon and the "red" of the unrefined sugar is the same as in English speaking countries.
What happened here is that Welsh has effectively two systems of color nomenclature. One is Ancient Celtic and the other is recent, largely borrowed from English. Gaelic in the Scottish Highlands and Islands is similar. But young people in Skye, according to reports I've read, tend to use the Gaelic words as "translation equivalents" of the English words. That is, they dont really have the Celtic system anymore -- just the Celtic words for English colors. But in Wales and Brittany, the Celtic system persists in reference to colors in the natural world -- grass, leaves, sugar, dragons, .... while they use words borrowed from English and Celticized or else loantranslations into Celtic words for man-made, i.e. culturally fabricated, colors. HOWEVER -- most Welsh speakers are bilingual in English. And Ive spent some time around them, hearing both Welsh and Anglo Welsh, and "standard" Midland or Southern Educated British English from them. When they use "standard" English, they use the English system and mean by "read" and "brown" and "green" what Englishmen and Americans mean. When they speak Welsh, the mean by "coch" and "llwyd" and "glas" what the Welsh and Bretons mean. So 'the Old Grey Mare" is Yr Hen Gaseg Las' where "glas" also includes the colour range "blue". cf Russian where you have no 'blue" but rather two words 'sinij' and 'goluboj". Welsh speakers in North America can sing "The Old Grey Mare" in one breath. And then immediately in the Goat Counting Song sing
Gafr las, las, las
'Goat "blue, blue, blue"....
but the mare and the goat are about the same absolute color.
Soooo ...you will have a hard time persuading me that these things have anything much to do with "mentality" or "the way of thinking". The Welshmen I know are not schizophrenic, not confused, and simply know two systems. Occasionally, when speaking Anglo Welsh, (a dialect of English, not Welsh) they'll use the Welsh system with a twinkle in the eye and a tongue in the cheek.
No, this kind of study is not very "popular" among linguists in North America. In areas like the one Ive just discussed, it gets a little more attention. But you cannot simply observe that two languages use what appear to be different translation non-equivaolents of the same thing and thereby conclude that people therefore "think differently". A great deal of the "literature" and a huge amount of the common Folk Prattle (especially common in university Language departments, particularly in Romance Language Departments for some reason) envolves just this kind of circular "deduction". But while it has not been "popular" among linguists, it has gotten a good deal more attention in Linguistic Anthropology, also often called Anthropological Linguistics though these are somewhat separate fields but with an intertwined history somewhat like a double helix. So look under those two terms too.
Someone once suggested that the Social Sciences and Social Scientists divide into two somewhat opposing and not entirely compatible groups or tendencies. The gooeys and the pricklies. Linguistics grew up in Russia largely out of literary studies -- the gooey end. Linguistics in North America and to a considerable extent in Britain had a rather different origin -- it grew either out of comparative-historical linguistics, rather hard nosed and concerned with evidence, and/or out of colonizers and explorers' contacts with languages quite different from anything they had known in Europe. (Had the Empress Catherine II had her way, Russian linguistics would have had a similar critical influence.). Both tended toward careful explicit descriptions of actual linguistic systems. The prickly end. Indeed, when you in your research look into things under "Linguistic Anthropolgy" be very careful. Some of this is very good and careful and does not leap to wild unwarranted conclusions and inferences about "how some other people think". But a good deal of it does and in more recent times, LA has not had vey much Linguistics in it, and not even a whole lot of Anthropology. It has rather become gooey-ly politicized and many of the writings are mostly about "words of real or imagined political power".
So my suggestion is that you read a lot and carefully and keep in mind that you cannot assume "mental differences" or "cultural ways of thinking" merely from differences in ranges of lexical items. Afterall, Russians have dusha but English speakers do have 'soul'. If there is a difference, it's probably theological and liturgical, not linguistic or "cultural" generally.
U of Cincinnati
Dept of Anthropology