I have two Chihuahua mixes who are flat coated so not the look of a poodle...one is 9lb and the other 14....my greyhounds have never had any issues with them. Occasionally it has turned into a bark fest in the yard with the littlest one barking at my greyhound Dylan. Then Dylan barks back at him but never like prey. I do not allow the little ones out in the yard with other greyhounds that come to the house.
When my boy Bounty got sick several years ago and I had just gotten Pixie, my fist chi mix, and she was a constant by his side as his cancer got very bad, very quickly. She really loved him.