You might try at SNO-Park system:
https://ohv.parks.ca.gov/?page_id=30701https://ohv.parks.ca.gov/pages/1233/files/2023-SNO-PARK_Brochure-WebVersion.pdfIt provides parking and restrooms at winter trailheads. This year be sure to check ahead to see where they have been able to provide services and what hasn't be cleared. November thru May, $15 per night or $40 per season.
On the east side the farthest south is above Tom's Place off 395 between Bishop and Mammoth. It is at 9000' and provides access to the Rock Creek basin. The Eastern Sierra Avalanche Center reporting area includes Rock Creek and provides daily weather and avalanche reports and predictions.
This year for sure, check ahead to see what is open.
Dale B. Dalrymple