not always. some do, but now-a-days most dont.
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.