I would not put holes in the roof drip edge. If you have gutters, then do as I do every year. Find those clever gutter plastic hooks that fasten to the gutter then dangle your ice cycles from those spaced hooks.
If you do not have gutters then go ahead and put holes in your underside wood area. I would install brass cup hooks every so often and Leave them in place instead of making new holes every year. This way you have non rusting hooks and only one hole.