First come first served state and national parks

Even if the roads are open, that doesn't mean access to the view points or trails. There's a whole lot of experienced people here advising you that April is too early and let me add my vote to that. My mother worked for years at the gift shop in the geyser basin, arriving in early to mid May. Often the drifts were 6' to 8' high. YNP is on a high plateau. Here in CO, some of the best skiing is in April. If you feel you must go then, might I suggest taking or renting snowshoes or x-country skis.