Could putting ice on your vein hurt you?

Not really: Ice makes blood vessels shrink up or try to close to reduce blood flow to the cold area - it's our bodies way of preserving heat. Putting ice over a vein will help stop bleeding from that vein. It also helps reduce inflammation in the area it is placed. Make sure you do not put ice directly against the skin - cover it with a cloth or other barrier to prevent injury from freezing.

No harm: Water ice will not cause any harm, even if placed overtop and obvious vein.