The great thing about Runes is how versatile they are.
You must learn the runes in order to use them. You can carve them on trees, or get a marker and write them on stones, you can even get a stick and draw them in the sand. It really is all up to you. If you dont want to utilize any of those methods, Ive found tremendous success just by visualizing a rune in my vision, and projecting it out in front of me while galdrring its name.
Ice magick sounds like an interesting concept. I think the most appropriate rune to engrave on your stav or wand would be the ice rune Isa. It is a solitary vertical line that symbolizes things of stasis or unmoving rigidity. That should fit easily on your project.
The real question would be what kind of spellwork could one do with sort of thing? I am thinking of perhaps freezing something in place such as ones will to stay on course or to stay focused on a task. Perhaps to solidify a relationship, or to freeze the energy of change to keep something just as it is. The power of the rune Isa has a variety of useful qualities.
Good luck and let us know what you create and how you have decided to employ it