arches to yellowstone

In Yellowstone, they try to get a few roads open by mid-April, but if you want to see much, you'll need snowshoes or Yaktrax. My mother used to work at the old Hamilton Store by Old Faithful and she'd often get up there in mid to late May with snow six feet deep. The CG's around Flaming Gorge won't be open in mid-April and snow will still be piled around there, also. They'll have camping at Dinosaur NM and snow shouldn't be an issue that time of year. It can be hard to imagine, but winter lasts until May (or later) in many mountain ranges in the west.

BTW, make sure you have your reservations in hand for Arches. April is a very busy time there.