You have it pretty well figured out. As others have mentioned, there were movements between summer and winter pastures, as well as to market for both sheep and cattle. The market movement would have been predominately in the fall... as young lamb and calves are born in the spring, and hay and pasture get scarce in the fall.
As for how much of each, the Rio Grande had a pretty high number of double deck cars back in the day- suitable for sheep and hogs, but not cattle. And I have also read references that Chama and Placerville (on RGS) both held records in the day for most head of sheep shipped in the US.
Things have changed- both transport method, and populations of cattle and sheep in general. Lamb has lost a lot of market share, and consequently, there are not nearly as many around anymore.