This paper makes me think the cartridge-conversion process was not totally complete until 1869, though significant numbers of cartridge-converted rifles would have been issued starting in 1867. The paper does not offer much insight into how it was decided which units would get the converted rifles first. I suspect frontier troops living in relatively close proximity to Native Americans would have been highish priority, but I don't know. The paper indicates natives were caught off-guard by the use of breechloaders in a battle the following year in 1867, so maybe the use of those weapons was unusual then.
Here's
another useful link about the weapons of a 1866 battle.