In the 1850s and 1860s, there were four known veterinary schools, in Philadelphia, Boston, New York, and Chicago. As well, your ancestor may have apprenticed to a veterinarian somewhere in Wisconsin, which was an acceptable way of gaining an education at the time. There also may have been private schools which advertised in rural communities, but were not known to the general community.
Also, before 1849 (when your ancestor was 19 years old), Wisconsin was a territory that included the eastern portion of what is now Minnesota. So, for example, Saint Paul MN was in Wisconsin Territory. Your relatives would likely have referred to that as "Wisconsin", but not the state as we know it. This may affect where you look for his records.