Pony-trekking is riding through the countryside on ponies — along tracks, over hills, through fields — not just going round and round in a riding school. It is often a holiday activity. The word is especially British. In the US people more often say trail riding. It feels outdoor and a little brochure-like: farms and guest houses offer pony-trekking. You go pony-trekking; the ride itself can be called a pony trek. You may also see it written pony trekking, as two words.