The Short Answer
Most Kashmir day tours from Srinagar are already small private or near-private trips by default, since group departures are less common here than in Southeast Asia — so the real question is usually private with a dedicated guide vs. a cheaper shared-driver transfer. A private Pahalgam day trip with a guide runs around $296, versus a private Gulmarg day trip with a guide at roughly $254. A bare shared-driver day trip to Gulmarg with no dedicated guide runs as low as $40 — a very different, much more basic product. Multi-day private Kashmir circuits (Srinagar-Gulmarg-Pahalgam, 7 days with transfers and guide) run $1,500+ for the trip.

From Srinagar: Private Pahalgam Day Trip with Guide
A real example of a genuinely guided private day trip, not just a shared transfer.
From $296
8 hours