Not on TD status. A TD spouse may live and study in the United States but is not employment-authorized, and herd management is not a listed TN profession. He would need an independent route, or the household must plan on one income.
TD permits presence and study, not a farm job
The dependant category attached to TN is TD, and it carries no work authorization at all. That rule does not bend for agricultural work, for unpaid help on the practice's client farms or for a job the employer offers informally. A herdsperson whose training came through apprenticeship and experience does not fit a listed profession, so a TN of his own is unlikely unless he also holds a qualifying degree in a listed field such as animal science. Other categories depend on facts he may or may not have: a year inside a corporate group for L-1, or capital to invest in a real enterprise for E-2. Children in TD status may attend school but likewise cannot work. The practical decision for a Kent household is whether the veterinarian's salary supports everyone, or whether the partner's route should be resolved before the family moves rather than after.
Hypothetical example: a Canadian dietitian accepts a temporary U.S. hospital assignment while her spouse hopes to provide paid nutrition coaching online from their apartment. The first review separates where customers sit from whether the dependant is authorized to work. TD status does not authorize that activity. The household must either defer the work, identify an independent status, or change the move budget; invoices or a Canadian bank account do not change the underlying restriction.