I live in Scotland, where the entire country has less people than Dallas/Fort-Worth - and even here 1k people isn't a 'small town', it's a village.
The town I grew up in had a population of ~35k, and it was definitely a 'small town'.
These things are all relative to your local norms, but I think demanding that 'small towns' have at most four people and a lame horse is excessive.