Why is "country" not pronounced like "count-tree"?
Why is country pronounced /ˈkʌntɹi/ and not /ˈkaʊntɹi/ ?
The sounds /aʊ/ (as in "how") and /ʌ/ (as in "hunt") have a historical relationship in the English language. Often, /aʊ/ comes from Middle English /uː/ and /ʌ/ comes from Middle English /u/. These are long and short versions respectively of "the same" vowel.
In historical languages related to French, the sound /u/ could be written as "o", "u" or "ou", more or less interchangeably. (There may have been some amount of consistency in any one particular document, or some criteria for which one to use in what circumstances within a single document, but I don't know about this.)
As a result of influence from French (-related languages), the digraph "ou" became established in Middle English as a way to write the sound /uː/. (I go over this in my answer to Why does “ow” have two different sounds) Some words taken from French with /u/ were pronounced in Middle English with long /uː/, for whatever reason, so in modern English they have /aʊ/, like count and round. Other words taken from French with /u/ were pronounced, at least eventually, with short /u/, like (apparently) front, so in modern English they have /ʌ/.
The use of "ou" in the spelling of words that have /ʌ/ in modern language therefore seems like it could be explained in a couple of ways. I don't know which of the following is the right explanation for "country":
it could be a retention of the French spelling. In French, "ou" was used for /u/; the use of the digraph for long /uː/ in particular is, as far as I know, an innovation that arose when "ou" came to be used in the spelling of English words. Other French-derived words where "ou" represents /ʌ/: double, trouble, couple
the similarity of the sounds /uː/ and /u/ caused some interchange between "ou" and "u" before English spelling conventions were solidified
the word used to be pronounced with long /uː/ in at least some varieties of Middle English. The modern pronunciation with /ʌ/ descends from a variant pronunciation with short /u/ that existed for some reason
The last one seems plausible to me, because a variety of vowel-shortening processes are known to have been active in English. For example, the word "southern" is pronounced with /ʌ/, unlike "south" which has /aʊ/, due to a sound law that has been called "trisyllabic laxing". Figuring out exactly how and why vowel-shortening occured in a particular word can be difficult, however: note that "southern" doesn't have three syllables in modern English. The "trisyllabic laxing" explanation only makes sense historically.
With "country", it seems likely that the cluster of three consonants "ntr" exerted a shortening effect on the preceding vowel. Janus Bahs Jacquet's answer to Why is ‘i’ in milk pronounced differently from ‘i’ in find? mentions child vs. children as an example of this kind of shortening before certain kinds of consonant clusters.
However, if the vowel was originally short in Middle English, not a long vowel shortened by a rule, this might be explainable by reference to the stress. The OED notes "Stress on the final syllable [..] was common in verse in Middle English"; there is a general tendency for unstressed vowels to be short more often than stressed vowels. A similar example might be "compass" /ˈkʌmpəs/ from French "compas" and the old pronunciation of "conduit" as "KUN-dit" (A Critical Pronouncing Dictionary, John Walker, 1791).
On the other hand (or back on the first hand), we do see /aʊ/ in the words "fountain" and "mountain," from French fontaine and m{o/u/ou}ntai(g)n(e), which I think supports the consonant-cluster explanation over the stress explanation.