Indeed, if you have the money - you can buy racing speed horses and in many countries it's still legal to ride them on the road while abiding standard road rules and avoiding highways. (The term 'Enterprise Horse' came to mind and I had a giggle)
You want a Suffolk Punch boiy[sic][1]!
https://en.m.wikipedia.org/wiki/Suffolk_Punch
[1] boiy, or some spelling there of, is how old fellas round these parts (Suffolk, England) like to refer to each other. :)
For anyone wondering what a proper young old boy sounds like I would suggest the following factual and totally legit documentary on the storm of 1987 ...as described by one "Brian from Melton":-