It varies from year to year, but Tioga Pass, the road between Lee Vining (adjacent to Mono Lake on the East flank of the Sierra) and Crane Flat (the junction of Highway 120 and Big Oak Flat Road in Yosemite) typically closes for the winter following the first major snowstorm of November. But, since that road climbs to nearly 10,000 feet in elevation at the park boundary, it can close short periods even in summer due to snow.
Yosemite Valley and Wawona are open year-round and accessible via three roads: Highway 120 from Groveland, 140 from Mariposa and 41 from Oakhurst.
Yosemite Valley is at 4,000 feet in elevation, and while it can have snow in October and November, it usually doesn't last long. But while it is snowing and for chilly periods following the storms, conditions can trigger chain controls, ie. you need a set of chains to be granted access to the park.
Of the three roads open year-round, Highway 140 is considered the All-Year Highway because it doesn't climb above 3,000 feet before reaching Yosemite Valley, though it currently has a size and weight limit due to a detour around a rockfall that happened last year.
The pros: It is gorgeous in Yosemite Valley in late October and early November, which is when the foliage peaks. Snow can make things even prettier.
The cons: It is a long drive from the East side that time of year. 5 to 8 hours depending on where you start and which route over the Sierra you take. You may have to go as far north as Tahoe, or south to Bakersfield to make the east-west trip over the mountains.