The word trekking is used far more by our American cousins than the British these days. The dictionary definition is "To make a long arduous journey" or "To journey on foot, especially to hike through mountainous regions" .
I have have been trying to establish why "Trekking" it is more commonly used in America, one reason might come from the origins of the word. The Dutch word to travel is "trekken" and the Dutch settlers in what is now South Africa used the word "trek" as a measure of distance to describe the distance travelled in one day by ox drawn cart. When the British Empire incorporated the Boer lands, the British language then absorbed many words from the Boer language. The connection to America is that of course when America was colonised the settlers made "treks" across the Great Plains of the United States and this is how the word was cemented in American English, good theory anyway!
The phrase "Pony Trekking" originates from Scotland in the 1955 when highland ponies were used to carry people on trips throught the highlands. The highland pony is a particular hardy mild mannered pony used for centuries by crofters to on their highland crofts.