We went in Mid April a few years ago and hit a snow storm. It dumped a foot of snow overnight so many of the remote places to visit were closed but the main attractions were all open. It was cold and windy but very beautiful with the snow adding to already spectacular vista.
We took a 4 day tour package from Williams (Good RV Park) rode the train to the Grand Canyon first train of the day so we crossed virgin snow. Stayed at the Grand Canyon for two nights in a hotel and then back to Williams on the train.
Crowds were minimal. Walkways were free of snow so it was easy to get from one place to another.