Monday, June 29th, 2020 - Dayhike of White Mountain Peak
First, a note about the drive up to the locked gate, which is almost the entire reason for this post. Yes, the unpaved portion of the drive is indeed long, and would certainly be best experienced in a vehicle with plenty of clearance and sturdy, off-road tires. That said, employing zen-like patience and some real experiencing off-roading in a variety of conditions, I succeeded in driving to the locked gate and back in a 2017 Prius without sustaining any damage. And I travelled so slowly, that the gas needle did not even budge. Can I recommend it? No. But I do not think that your choice of vehicle should necessarily deter you from the trip.
Second, it was seriously windy. I was not alone in thinking that it was a beautiful day for this as there were two other cars when I arrived at the end. I caught a glimpse of a pair heading up just before they disappeared around a bend and I followed about ten minutes after they took off. I had no problem making it to the weather station just above the Barcroft research station, and once there I could see that there was no snow save a small patch off the trail below the summit. I continued on across the flatter, more exposed plateau and ultimately turned around because of the wind. In milder conditions, I am sure that it would have made a great day hike.
On a side note, I would love to know the rationale for the random quarter mile or so of paved road near the entrance to Patriarch Grove. Bizarre.