As I've presently imagine it:
The country isn't so much mountainous as it is hilly. I suppose the skiing there isn't great and maybe limited to several weeks at most. I describe it as a place where snow falls, but where wild palms and citrus can grow in a microclimate. Part of it is a swamp that leads to the coast. There isn't a natural harbor, and the water nearby is too shallow, but at least they have air access.
They were occupied until the early 20th century. Lead by a great leader (and maybe with a few Americans who aren't all that pro-American) employing strategies and at times brilliant tactics against their indolent and incompetent occupiers, they get independence.
They make a treaty with this country and 3 others. These countries together might be the size and area of one of US's smallest 40 states.
The guerilla leader turns out to be a good political leader, who at the beginning might be semi-authoritarian. He pursues strong neutrality and self-reliance, and with mixed results, industrialization. There is probably conscription in the first few decades. They declare war on Germany in very late March/early April 1945 (they also try to figure out what to do with their millions of Reichmarks).
Why didn’t others invade?
They have hills and swamps, unique language, decades of self-reliance and some preparation, and pretty well no natural sources of petroleum and natural gas.
What about an economic blockade?
A US battleship might get run aground if it comes too close, aircraft carriers (IIUC) are expensive to run, and a smaller ship might get sunk by them and force a more intense response from the US. IIRC, Bill Clinton was less interventionist than Bush (either of them), Dubya Bush was too busy with Afghanistan and Iraq, and under Trump, Hasan Piker might spend a week or 2 visiting the country and giving autographs, yelling "Viva la [name of the country]!".
Strong economic ties to many countries, neutrality in wars, value outside economics (craftsmen).
They buy from pretty well everybody (with maybe some not too costly tariffs), sell to pretty well everybody, and are neutral (today they trade with Russia while maybe 100 of their citizens are in Ukraine's international battalions).