Anything before May is asking for snowstorms or worse in high country. I've been snowed on July 3rd at Craters. The North Rim of the GCNP won't even be open then, the South Rim will but may have deep snow. This winter is looking like another very cold and snowy one. Snowfall records have already been broken in Montana and they have had significant snow all the way down into CO and CA. Very early snow.
Last year's snow hasn't even melted in some places which is also unusual. I'd aim further south if the time frame is rigid, lots to do in southern AZ and NM. It's the perfect time to visit Big Bend NP in TX. I would not want to be caught in a blizzard in that class A on a mountain road.