Once upon a time, a friend of mine who lives in Switzerland offered to meet me in a Yellowstone springtime to take pictures for my guidebook. He wrote that April would be a good time for him. But no, I wrote back, in April many roads are still closed, and the chances of more snow are still quite great. The park is totally closed for road plowing and other maintenance until mid April, and most facilities don’t open until some time in May.
Today we are four days past the first day of spring in the northern hemisphere, but this 
is what I found this morning on the Old Faithful webcam.
You will understand why spring is so late in Yellowstone, if you factor in that most auto-accessible areas in Yellowstone are at 7,000 to 8,000 feet (about 2,100 to 2,400 meters) in altitude. This spring the park roads will begin reopening on Friday, April 20th, when the West Entrance to Madison Junction, Mammoth Hot Springs to Old Faithful village, and Norris to Canyon Junction roads will open. Higher stretches of road open throughout May, with the last being the Northeast Entrance / Beartooth Highway opening on Friday, May 25th, for Memorial Day Weekend.
This summer season you can expect construction delays of up to thirty minutes on the five-mile stretch between Apollinaris Spring and Roaring Mountain (Mammoth to Norris road); on some parts of the rim roads and trails at the Canyon of the Yellowstone; and along the East Entrance Road between Indian Pond and Fishing Bridge.
Year-round, for Yellowstone road conditions, take a look at this NPS park roads website. Or you may receive Yellowstone road alerts from the National Park Service on your mobile phone by texting “82190” to 888-777; an automatic text reply will confirm receipt and provide instructions.