Greyhound, whippet and IG heads are actually smaller than their necks, so they can slip out of their collars easily. I wouldn't walk mine on anything that wasn't a 2" martingale. Cinnamon especially knows the trick up back up and flail like a fish to get loose. She WILL if it is at all too large!
Coats are a big thing for these breeds. They have such thin fur and so little body fat. They truly get cold quickly.