The North Rim opens on May 15th. Sometimes the snow has melted before it opens, sometimes it hasn't. But it's nice to use that as a guide to when there will be services available.
Winter snowpack in Arizona is highly variable.
There are a handful of automated snow-depth stations in Arizona. You can find them at this website which will show you current snow-depth as well as a few other variables such as percent of normal (which can help you determine how things are going based on reports from previous years).