I think a dog just needs to have good training BEFORE you start working them with a horse. I had a Basset Hound (yes a Basset) and he came to work with me at the feed yard and he mainly stayed close to the water bowl until we started bringing cattle out of the pens to move them. Eli moved right in behind the cattle and started working them as only a Basset could do. He was not aggressive and he sure watche out for not only the cattle's feet but the horses as well. He would always follow in the heel position when he followed me around but he didn't go very far with us because he just didn't have the endurance. He did like to work cattle with us and when we loaded out, he was really good at "telling' the cattle to move with his baying...lol. (Eli passed in December 2008 in a terrible accident and I never got pics of him walking with my horses and working cattle).

Now I have a lovely Border 'AL' and she picked it up perfectly to work with my horse and me. She keeps a distance and follows me EVERYWHERE when I am horse back. We rode home on horse back after work last week (15 miles one way) and we took 3 hours because I didn't want her to get tired on me. (We did 24 miles one day and the last 6 miles she started getting tired.) She isn't too keen on riding in the saddle with me yet but she is improving.

I think the breed of the dog makes a difference too. Big dogs can be a problem if they get worn out, you have to stop to let them rest. But Borders, Aussies and the breeds that size are manageable in the saddle.

Take time with your dog. Get good training and control before starting them with a horse.
Good luck!