not always. Some do, but now-a-days most don't.
Here are some of my STBs:
These ones are my roman noses. The roman nose is actually becoming a throwback to older STBs. Its disappearing more and more now.
My 2 yr old La'Don Belle:
My 7yr old mare, Sumaturo:
Here are our STBs without roman noses:
5yr old mare, Hopedale Jive
6yr old gelding, Talbotwesternflame
13yr old retired racehorse now broodmare, Slim N Fit
STBs now have a huge range of face shapes, body shapes, height, etc. And to think, their lines can ALL be traced back to ONE original STB... Hambletonian 10, also known as Rydysk's Hambletonain.