Big trees has two campgrounds, the North and South Grove, with a total of 129 campsites. For Reservation go to recreation.gov six months in advance. For more about Big Trees check it out in the destination guide.
In spring and fall it rains, thunderstorms or snow showers are likely, it is drier in the Fall. The South Grove is closed from approximately mid-November to mid-April. The North grove area is usually open and sometimes suitable for cross-country skiing.
Calaveras Big Trees became a State Park in 1931, more about it is here.