I'll echo -- switch Bakersfield and Sequoia
You'll go through Bakersfield before you get to Sequoia. So I'd recommend spending the night somewhere around there.
I will note the road going up the west side of the Sierras to Sequia past Moro Rock (not to be confused with Morro Bay...) is a narrow winding 2 lane mountain road. I'd recommend hitting it in the day time, particularly if you're tired and not really used to driving on the wrong side of the road.
You might consider staying the night in Visalia rather than Bakersfield -- its the last reasonably sized down before you head up into the Sierras. (And otherwise, there's nothing amazing in my experience to recommend Bakersfield, other than its a larger town with perhaps more options...)
Now, there is a chance of snow in the Sierras in March. March can be a wet month in California, and if there's a storm you can get snow in the Sierras. I went to Sequoia a couple of years ago in April, and stayed in the Wupatki Lodge in the park (discounted rates in the off season), and followed a storm up the mountain the next day. The roads were plowed and dry, and it was a really beautiful sight with around 6" of snow -- but if I had been a day earlier it would have been either chains and a low crawl up the mountain or road closed until the snowplows came through. Just don't be surprized ... it is a possibility. Same with Yosemite.
Other than that -- its a pretty good bet that taking the southernly route through Barstow to Bakersfield you won't see snow other than on the tops of the mountains. Sometimes they'll get a dusting of snow down in the high desert in December or January -- but its time on the ground is measured as a couple of hours when the sun comes up.
No Road to the National Park
Sherman Pass is a fine road, and I've driven it myself. In fact, it dumps out near one of my all time favorite little dispersed camping spots in all of California. Going West to East, it is also a great road for enjoying a very abrupt change from Mountain to Desert Views.
But While Sherman Pass takes you through Sequoia National Monument and the Sequoia National Forest, it does not take you into Sequoia National Park.
To get to the National Park from Sherman Pass, you still have to go all the way out to Porterville, and then take CA-65 up the East Side of the Central Valley, and then go back East to enter the National Park.