As for April in the Sierra - there is snow on the ground but day temperatures are moderate. This is actually a good time of the year for a multi-day ski-tour. But you still need the right kind of winter equipment and experience. You would most likely be camping on snow at anything in the mountains.

In a normal snow year, April 1 is considered the peak snowpack for the higher elevations. Memorial Day weekend (end of May) here is considered the start of the backpack season. Even then, a lot of the mountain passes are still closed.

Tahoe Rim would be a ski trip.