super secret about the Grand Canyon and phantom Ranch - if you are a small party and don't mind lodging in the dorms you can walk up the day of your hike and generally get in. It's worth taking the chance otherwise waiting list is 1 - 2 years...
Also we usually do the trip in February and March - yes lots of ice and you may get snow, or rain... buy some cheap shoe spikes and keep them in your pack. They are like mini-crampons. With the spikes ice is no problem.