If you want to suggest earthiness, ruggedness, stability and strength, brown is a color to consider for your veterinary logo. Few people claim brown as a favorite color and it is the least-used color in brand logos. Brown is considered a masculine color and can be associated with dirt and decay, but it can also be used to convey comfort and simplicity.
Although probably not the best choice as the main color for a veterinary logo, shades of tan work well as a second color for predominantly blue, green, red, purple and black logos.