Does "traditional" Chinese food differs from one country to another?

It is not whether it is served cold or hot that differs.  All ethnic foods (and not just Chinese foods) outside of their nation of origin are changed to suit the preferred taste of the locals. it is very rare to find any restaurants that serves foods exactly as how they are made in the country where they originated. Did you seriously think pizzas in Italy are like those in the US? You may be surprised that pepperoni in America is not the same as pepperoni in Italy. And did you think American foods will taste the same in other countries?

The reasons are very simple:

1) restaurants are in business to make money and they cannot do that if they serve foods that most of the local people are not going to like. If they are in America, they have to make it palatable to American tastes. If they serve American foods in Japan, India, France, etc. they also have to change it to please the people there.

2) Even when a restaurants wants to recreate the dish exactly, they may not be able to do so because the ingredients (especially fresh ones) are not readily available. In most cases, they have to settle for canned or dried variants which alters the flavor of a dish.

3) Some dishes that have ethnic names were never invented in the country people associate them with. For example, chicken parmesan was invented by Italian immigrants to the US, but the dish did not originate in Italy. The same with Chop Suey which was invented by Chinese immigrants in the US and no such dish existed in China. And California Rolls you find in Sushi restaurants obviously did not originate in Japan.

You may be disappointed by this, but I have lived in 5 countries and travelled to many more and I can tell you some of the "authentic" dish do not taste very good to me. And that is because different people have different preferences. It doesn't make things bad or good, but it is what it is.

You are correct.  Even the Chinese food between Canada and America is different, or different parts of each other those countries. It's "localized" or regionalized.

Chinese food from China is not remotely close to American Chinese food. Typical take out Chinese food is pretty much the same all over the US, and has all the standards meat like pork, chicken, lobster, etc. You will Never see Dog or Bat on an American Chinese food menu. 

I am a chef. And my local Asian grocery has an Enormous Fresh meats section. Many of the 'meats' I have never even Seen before and wouldn't have a clue how to prepare them. Those ingredients Scare the average American and would Never show up on an American Chinese Food menu. 

Traditional Chinese food varies around China.

Outside China; it's often not traditional Chinese food.