Help: Driving to Jackson Hole from Idaho Falls in late November

Hi! I'm traveling to Jackson Hole to ski over the last weekend of November. Flights are significantly cheaper into Idaho Falls Airport. Though I looked into the shuttle with Salt Lake Express, the times do not work with my flight times, so I'm wanting to rent a 2WD car and drive to Jackson Hole. How likely is my need for a 4WD vehicle? I understand that the mountain pass can be prone to winter storms, etc, but if there is a route that can be taken to avoid sketchy driving, then that is also an option. Wondering if this is less of a concern that early in the winter season. Thank you for any advice!