Yes — Jeti-Oguz is one of the easiest scenic destinations near Karakol to reach, which is part of why it's so popular.
It's about 25-30km southwest of Karakol on a paved road the whole way to the gorge entrance, roughly 40-50 minutes by car. From the entrance, a further gravel road continues toward the "Seven Bulls" rock formation and the valley where horseback rides start.
A shared taxi from Karakol's bazaar area covers the paved section; from the gorge entrance you'll need to arrange a further ride or walk to reach the horseback-riding area and waterfall.
Because the horseback riding, the waterfall walk, and (for the overnight version) the yurt camp are spread across the valley, a single arranged transfer with a guide who knows the schedule is usually simpler than coordinating multiple local rides — especially if you also want the horse ride included.
Zoomy