I had to do a double-take, but I realized you're referring to the Malamute breed of dog. I highly doubt they were ever ridden into battle, and I will eat my hat if someone shows me evidence that they were.

However, you are touching upon something interesting in asking how effective big dogs are against horse cavalry. There is some debate on why breeds like the Irish wolfhound were originally made; such as unhorsing a horseman - but this is largely myth and there has been nothing approaching serious evidence supporting this. However, physically riding a Malamute or Wolfhund with a saber flashing will sadly remain in the realm of my juvenile dreams.

...I think the word you're looking for is "Mamluk" and I think you've probably played a lot of AOEII.

A mamluk is a type of soldier, not a type of... camel, maybe? There were mamluks of all kinds, including traditional horse cavalry mamluks. They were decently effective, as far as slave soldiers go.