I don't cover that area with snowshoes, but rather with cross country skis. If you drive up to Carson Pass proper, there are two Sno-Park lots, so have a permit. If you go north, you will get up around Showers Lake where you can see Lake Tahoe in the distance. But there is scenery even if you make it only halfway. Instead, if you go south, you will be heading toward Round Top Mountain. Lake Winnemucca is at its base. I see more snowshoe tracks going to the south rather than to the north.
If you need something easier, then drive on through Carson Pass and down to the Red Lake turnoff. There, the Blue Lakes Jeep Road heads south. If you follow it about 2.5-3.0 miles, you will get to some scenery. Again, many people turn around halfway.