Mattie Ross (Hailey Steinfeld) carries her father's Colt Dragoon, as is described in Portis' book. The gun used in the film is an actual percussion Dragoon, while the 1969 film used a cartridge-converted Colt Walker. I imagine the Walker was used due to its even more imposing size to contrast with Mattie's small stature. Still, I appreciate the adherence to the source material.
Colt 1851 Navy
Marshall Reuben J. "Rooster" Cogburn (Jeff Bridges) carries what look like Colt 1851 Navy revolvers during his famous charge.
Single Action Army
Rooster also carries what appears to be a Single Action Army of "Cavalry" length.
Winchester 1866 "Yellowboy"
An unknown member of "Lucky" Ned Pepper's gang wielding an Winchester 1866 "Yellow Boy", probably during the famous charge at the end.
Henry 1860
True to the book, Tom Chaney (Josh Brolin) carries a Henry rifle, stolen from Mattie Ross' father.