Pamela, spinning dog hair is fun, I've done it! Great of you to offer yours. :D Unfortunately short hair from cats and short-haired dogs is not really spinnable. I had a dog with even longer hair, and I could barely spin it, it was still too short. Well, it was doable, but it required a very fine spindle used for cotton that most spinners don't spin with. However, soft fluffy fur makes great stuffing for teddy bears and such crafty projects, so if you've saved it, you can use it for that!
Ooh, Ingrid, I bet that chow fur was a PRETTY color!
BTW, another fact about spinning pet hair: it's usually the undercoat, not the top, coarse fur, that is spun. The top hair can be spun too, probably good for sock soles, nice and durable. But the undercoat is the soft stuff.
If you want to spin pet fur, you can often get it free from a pet groomer. Ask them to save you the clean combings of a long-haired breed, like a collie. They wash the dog, then dry and comb it, and all they need to do is put it in a bag for you. Shedding season is the best time to get it.