It's sort of ridiculous to type a country, but I think that each time period in history has had its own zeitgeist, which can be assigned an MBTI type.
USA: Historically, INTP (Brief period after Declaration of Independence; founding fathers were secularists who valued individual freedoms and believed in open government. Populace was intellectual and freethinking.), ESTP (19th century; Wild west, industrialization, gold rush. Valued courage, independence, fearlessness.) and ENTJ (Early 20th century; business held in high esteem, new values, new art styles, very money-driven society.) 40's and 50's were ISTJ and ESTJ, respectively; tradition, hard work, patriotism were valued. During the '60s, the counterculture was ENFP (Peace movement, free love movement, new ideas, drugs and changes in sexual attitudes.), and became more ISFP during the '70s. From the '80s on, it's been ESFJ; religion, patriotism, strong work ethic were and still are valued.
Mongolia: During Ghengis Khan, INTJ. Society was very advanced culturally and economically. The empire was egalitarian and meritocratic. It was similar to the Roman empire in that, if you weren't with us, we'd burn your house and kill you, but if you were with us, you'd enjoy a level of prosperity and happiness that was unprecedented at the time. When the empire fell apart, the Mongolians and the Turkic tribes in Altai, Tuva, etc became more ISFJ; Very introverted society, placed emphasis on shamanism and tradition.
Rome: INTJ. Similar to the Mongol Empire but wealthier and arguably more powerful. Individual emperors had a great deal of power, so the specific type fluctuated quite a bit depending on the time period. I don't know what Italy is today... Probably ISFP.
Greece: Ancient Greece was ENTP; Obviously, philosophy was a big part of Greek culture. Art was too. Extroverted; people shared ideas openly. Now, I'm not sure. Maybe ISTP?
Russia: From the Kievan Rus until the USSR, it probably was ISFJ. Religion played a big part in people's lives. Heavy reliance on tradition. Most early Russian Communists were Ns; Lenin was an INFJ, I think. Trotsky an ENTP. During Stalin, it shifted towards ISTJ. (Stalin himself was an ESTJ.) Nowadays, there is a big focus on partying and night-life. People are very status-conscious. There is a pretty significant "counterculture", for lack of a better word, of pro-western intellectuals i.e. Kasparov who are NTs.
Germany: The Third Reich was INTJ. I'm tired from typing so I'm not going to elaborate.
France: INFP. Historically, has had a bustling culture. Fi-focused literature... Again, tired. Maybe I'll continue this later.