I have small veins too. Sometimes the Heartland employee looks at them and grimaces.
But it usually works out and I've successfully given blood many times over the years.
If someone seems especially nervous about your small veins, I would ask if a supervisor could do the draw instead. I've had people decide on their own that they would prefer a more experienced person to start my draw, or sometimes they try once and then if they're unsuccessful they get someone else. My impression is that there's often someone on duty who is the designated expert for situations like this.
I agree about staying hydrated--and starting to drink extra water a few days in advance.