When people discuss the need for crampons and ice tools, they often skip over the most important tool: the boots. A medium-weight boot with stiff soles is all you need on moderate slopes in warm weather. Adding a pair of ski poles lets you navigate slightly harder terrain. A pair of well-fitted strap-on crampons will get you up and down much steeper terrain. If you fall without an axe, you are going for a ride, but it’s possible to go almost anywhere without one. I’ve even done the Whitney Mountaineers’ Route in winter without using an axe.
Light hiking boots, trail runners, and other flimsy footwear work fine on the trail, but they are just about useless on snow. The flexible soles make it easy to slip. They don’t work well with crampons, and the crampons may even slip off the boot at the worst possible time.
I would take the stiffer boots, crampons, and hiking/ski poles. No axe. And you might not need the crampons.
You can melt snow if you prefer, but there will be plenty of liquid water.
