Ed;
If the battery lost about 30 horses on a road march of about 300 miles, this may imply they were pulling the heavier 12 pounder light field gun (Napoleon) but I still don't believe that this type of gun would be assigned to horse artillery. This is just a quick unproven thought.

If you or anybody else can detect in the picture you mention, what the muzzle looks like, The M1861 3" Parrott had a slight muzzle swell which the M1863 3" Parrott did not have. This is the only way to tell them apart without actually looking at the markings on the gun.

Ron