Weather is the key on US 395 or any of the California mountain highways. SR 4, 89, 108, 120 are closed for the season and 4, 108 and 120 probably won't open until Memorial Day (late May) at the earliest. SR 89 over Monitor Pass from South Lake Tahoe (US 50) and Carson Pass (SR 88) is opened when the snow melts and no storms are on the way. It's in the rain shadow of the main ranges of the Sierra, so the snow isn't quite as heavy and deep over Monitor Pass.
If you are coming from the south, LA, San Diego, Bakersfield, etc., you'll simply drive up US 395 but make sure you you have chains for your car, even 4WD, a shovel, etc. From Northern California, Fresno, Sacramento and the Bay Area, you need to check to make sure the passes are cleared. You have I-80 to Reno, US 50 through South Lake Tahoe and SR 88 over Carson Pass. Usually at least one is always open. I-80 is the major route over the Sierra and is heavily traveled by cars, trucks, busses. On some weekends in the winter, it's a big snarl and traffic backs up on each side for hours. US 50 isn't quite as bad for traffic and 88 has the least, but is the highest of the three passes and has the fewest services (gas).
Around Mono Lake in winter can be enchanting but pretty cold there in the basin. I've seen it with beautiful pogonip fog, a freezing fog which adds a rind of frost on everything. The nearest places for gas, food and lodging are Bridgeport and Lee Vining. Roads in the area are neither patrolled or plowed except the state and federal highways and a few of the more populated areas near the lake, so don't expect a rescue if you go beyond the plowed roads if there is snow. Cell service is also flakey so plan appropriately.
Stroms can hit any time in winter, so keep an eye on the weather reports or plan on staying a couple of extra days if you get snowed in. Gas, food and lodging are not cheap in the area, so bring extra $$, just in case!
Now that you are prepared, head on over and have a ball shooting that surreal landscape with a coating of nice, cold, white snow!