What is the name of the dangerous forest located near Ponyville?

The dangerous forest near Ponyville is the Everfree Forest.

The Everfree Forest is an enchanted woodland adjoining Ponyville. Unlike much of Equestria, it operates outside the normal rhythms of pony magic: plants grow on their own, animals look after themselves, and weather changes without the pegasi managing it. That unnatural independence is one reason the ponies regard the forest as threatening.

The forest is home to Zecora, a zebra who lives in a hut there and gathers ingredients for potions. It also contains dangerous creatures, unusual plants, the mysterious Mirror Pool, and the ruins of the Castle of the Two Sisters, where Twilight Sparkle and her friends first encounter Nightmare Moon’s history.

Readers sometimes confuse it with other wild locations, including Hayseed Swamp, Froggy Bottom Bog, and Whitetail Woods. Those are separate places. The Everfree Forest is the landmark immediately associated with Ponyville’s eerie neighboring wilderness and is often shortened in dialogue to “the Forest.”