Here's how I do it: (if you have safely worked with fiber reactive dyes you can skip ahead to the fun part!)
Now to the fun part!
Once the snow is packed in the tub, simply squirt the dye over the surface of the snow. I like to use 2 colors, one going in one direction and the other crosshatching the first. One color works too, as would three. Play! See what works for you.
Now comes the waiting. I leave this just inside the garage near the door where it is coldest for at least 4 hours. Then I move it into the studio to continue melting. It looks a bit like a snow cone, but DON'T EAT IT! :) In fact, it's a good idea to make sure this is out of reach of pets and young children. It looks yummy and they don't know better.
Snow dyeing is lots of FUN!!!