The color, size and speed, sound a lot like an Eastern Coachwhip Snake (which is harmless). Usually Eastern Coachwhips on the east coast are darker by the head than the tail and are orangey-tan over anywhere from 2/3 to most of their body.

By the description that would be my guess. If you do get a picture (it doesn't have to be high quality or a close-up) I can confirm that for sure. In any rate, it doesn't sound like anything venomous or dangerous to a Scottish Terrier.

I looked it up in some Google images and if there are times when the darker color toward the head is not so noticeable, then that must be what it was. (My getting a photo is unlikely since I tend to not think clearly when I encounter a snake. ;> )
Thanks Wayne!