June or July it is. We've got a "normal" snowpack per yesterday's survey, so April-May weather will tell the tale. A hot, dry spring will clear a good deal of it and if the March weather continues, it'll be just that. In any case you're unlikely to need snowsnoes, as the snow will be quite consolidated by the time you go, but some kind of traction might be warranted (instep crampons, Kahtoolas, etc.). Ice axe? Probably not.
You *will* want bug and sun protection! With the nice long days you'd probably be able to cover some serious mileage.