I have participated in Cowboy Action matches for several years and, with the clubs I have shot with, I have never had a stage where you would have to reload your rifle. Most stages are written for 10 rifle rounds, but occasionally will call for only 9 rifle rounds. I would imagine there have been stages written that involve a bonus rifle target where you might have to load an extra round on the clock. The most common reload during a stage is with the shotgun and I have shot in a few stages where it calls for you to load an extra pistol round on the clock for a bonus target...
I have a Uberti 1860 Henry in .45 Colt with a 24-1/2" barrel that hold 13 rounds in the magazine tube and a Uberti 1873 that holds 10 rounds. I have seen a few shooters use the Henry Big Boy rifle in Cowboy Action matches, but most shooters seem to use an 1860, 1866, 1873 variation or a 1892 lever action.