Are there any Christians who understand Daniel 10 implying that there is an evil spirit prince over each country? The angel (I believe it is Gabriel) says:


  "Soon I must return to fight against the spirit prince of the kingdom
  of Persia, and after that the spirit prince of the kingdom of Greece
  will come."  (Daniel 10:20; NLT)


This assumes an evil spirit ruler over both countries and possibly more.  Are there any Christians1 who understand Daniel 10 implying that there is an evil spirit prince over each country?

1. Any Christian meaning a particular Church or group, etc.
To the question 

Are there any Christian traditions that speak of single nations being under the protection of an angel?

The answer is yes. There is the common view among Church Fathers, consistent with Jewish Rabbis, that angels are entrusted to the spiritual care of kingdoms/nations.

This article NATIONS AND LANGUAGES, THE SEVENTY: | Jewish Encyclopedia says:


  According to the Rabbis, each of the seventy nations is placed under
  the protection of a special angel, except Israel, whose protector is
  God Himself (Gen. R. xxxvii.).


And this article Angels | New Advent says:


  Such appearances of angels generally last only so long as the delivery
  of their message requires, but frequently their mission is prolonged,
  and they are represented as the constituted guardians of the nations
  at some particular crisis, e.g. during the Exodus (Exodus 14:19;
  Baruch 6:6). Similarly it is the common view of the Fathers that by
  "the prince of the Kingdom of the Persians" (Daniel 10:13-21) we are
  to understand the angel to whom was entrusted the spiritual care of
  that kingdom, and we may perhaps see in the "man of Macedonia" who
  appeared to St. Paul at Troas, the guardian angel of that country
  (Acts 16:9). The Septuagint (Deuteronomy 32:8), has preserved for us a
  fragment of information on this head, though it is difficult to gauge
  its exact meaning: "When the Most High divided the nations, when He
  scattered the children of Adam, He established the bounds of the
  nations according to the number of the angels of God".


I do not know when the guardian angels of the nations got their commission to explain some fallen angels being princes of certain nations.



Endnote

The Jerusalem Bible Popular Edition note on Dan 10:13 has:


  Michael ('Who-is-like-God?') is the guardian angel of the people of
  God.