You are all correct. There are only two convenient routes to travel between San Francisco and Las Vegas during the winter. The northern route goes northeast from San Francisco on Route 80 to the Donner Pass near Lake Tahoe and Reno Nevada, then south along the eastern side of the Sierra Nevada Mountain Range and through the deserts to Las Vegas. The southern route goes south through the Central Valley of California to Bakersfield then west through the Mojave Desert below the edge of the Sierra Nevada Mountain Range to Las Vegas via Barstow.
Between the northern crossing of the mountains at Donner Pass and the southern crossing below the mountains at Barstow, there are about 300 miles of impenetrable mountain barrier with no open passes. All of the passes between those two routes are typically closed between October and May due to heavy snow accumulation.
The southern route is the safest. There is little chance of snow in the low altitude Central Valley nor in the 1000 meters high pass between Bakersfield and Barstow. Snow is also unlikely in the Mojave Desert to Las Vegas. In December 2008, Las Vegas actually had nearly 20 cm of snow, but that is a highly unusual occurrance that happens but once every five years or so.
The northern route goes through Donner Pass. At 2,000 meters, Donner Pass can get a lot of snow in the winter, but the highway maintainence crews typically keep Route 80 open at all times. The pass may close for a few hours or even a day during a severe snow storm, but it quickly reopens. You might be required to put chains on your tires when driving through the pass.
There are great scenic attractions along both routes, but they may be difficult to approach. Along the southern way, you can detour into Yosemite National Park or Kings Canyon and Sequoia, but that requires driving into the higher altitudes of the mountains where the risk of snow filled roads becomes greater. Along the northern route, you can pass by Lake Tahoe, the Mammoth Ski Country, Lake Mono, the ghost town of Bodie and through Death Valley, but this route will take you through some high altitude roads with snow dangers.
If you monitor the weather reports along the way and drive carefully, it will be well worth the risk to see some of this fabulous scenery during the winter.