I recently made a reservation through recreation.gov to camp in the yellowstone backcountry one night in the beginning of May. It would be in the Lamar Valley (Slough creek). Here's to hoping it will be snow free by then, but I suppose bringing snowshoes would be a reasonable precaution?

I was asked a bunch of info such as where I'd be entering from and where I'd exit the day after, where I'd pick up the permit, vehicle information etc.

What is unclear to me is whether the reservation is all set and I can just go pick up the permit come May, or there is a process taking place whereby my reservation can either be approved or denied?

Additionally (and this may be a long shot), does anyone have recommendations for a camping spot in/near Grand Teton that is potentially snow-free at the start of May?