When I was looking for large animal experience, I contacted every equine-related vet at UC Davis and sent them all letters begging for experience. I was willing to work for free and do any grunt work necessary. I did this a year ago and was able to perform independent research on the bacteria that causes pigeon fever in horses (hopefully it will be published!), assisted in a pharmacokinetic research of Ciprofloxacin as an oral antibiotic for horses, and helped out in a metabolic performance test on horses during the Tevis Cup. But my biggest project has been helping out with research as to why horses in the Salinas area are afflicted with osteoporosis, some even being euthanized at the age of 4. With this project, I helped out during necropsies, nuclear scintigraphy, radiographs, and tissue debridement of affected bones.
I did all of these projects during school and throughout the summer while caring for our two young sons. I was given such awesome opportunities after the vets saw that I was willing to work hard, come in early/late/on weekends, and was dedicated to the project itself. Two of these positions later turned into paid positions that I am still helping out with and I received a couple of really awesome letters of rec (at least both vets told me they were awesome...).
My advice is to put yourself out there and create your own opportunities. One position that initially sounded dreary (growing bacteria in dirt??) turned into 4 excellent projects that I learned so much from. Find an area that you want to work in and throw yourself to the people in that area. Persistence pays off, and something will work out. But, be prepared to work your butt off!!
Hope this helps & good luck!