I get to say this a few times every spring. Yes, while there is still snow on the trail, you need to carry an ice ax and crampons. You may not need to use them if conditions are good the day you climb. If the snow gets icy and you climb without them, you will not be able to summit, or even worse you may get hurt. They only add a few lbs. to your pack, don't be afraid to carry them.
Proper use of an ice ax and crampons is not rocket science. Either Google the subject or get a copy of Freedom of the Hills, and read the self-arrest section. Before you leave be sure your crampons fit your boots correctly, and/or have the tools required to adjust them with you. Practice arrest in your head as you move up the trail over and over again. Then when you find a short snow covered slope, practice a few times. It’s not hard to learn.
