Volunteer with a student group or non-profit working on issues involving farm animals. Even the smallest college towns are likely to have chapters of animal welfare or advocacy organizations. In rural or remote communities, the issues facing these organizations are often related to farm animal welfare, and working with them can give you the opportunity not only to encounter farm animals but also to contributing to their well-being.
Investigate opportunities at your college's agricultural or veterinary schools. Enroll directly in classes or programs if you are interested professionally in the field, or inquire about extracurricular opportunities if you do not want to make a formal academic commitment. Contact your school's biology or ecology departments if your university does not have a dedicated veterinary school and stress that you are interested in working with live farm animals. Many schools keep live farm animals on campus for experimental or study purposes and will appreciate any help you can provide in caring for them.
Look for farms in the area. Contact farmers in surrounding rural communities and ask if they need any help managing their animals. Many farmers may even be willing to offer you a paid job if you can devote a significant number of hours to it every week.
Devote your summers and breaks to working with farm animals. Take advantage of the flexibility that college provides to pursue your interests outside of the academic calendar. Volunteer for organizations that work with farm animals during breaks and look for scholarships or volunteer funding at your school that may even offset some of the cost of participating in the projects.