The military model 1860 Army had a steel backstrap because a shoulder stock could be mounted to it. Also most if not all 1851 Navies made at Hartford, CT. had "iron straps" if they were set up to take a shoulder stock, which was less common. However the Army did buy some iron-strapped 1851's that weren't designed to take a stock, and these were supposedly made from surplus parts brough back from London after Colt closed his Armory there.
In Colt catalogs and price sheets, the word "straps," refers to the backstrap and trigger guard. On most percussion models, excluding the Walker and Dragoon's the straps were made from cast brass. Those sold to the military services were usually plain brass, while commercial products were silver plated - which looked good when the revolver was new but quickly wore off with use except in protected areas.
Another exception was the U.S. Navy, which bought many iron strapped Navies, later had them converted to metallic cartridge (.38 Long Colt) and kept them in service until 1888.
So far as strength is concerned, Colt used brass for a long time with apparently no problems, but when the 1872 "open-top" .44 cartridge revolver came along, shortly followed by the 1873 Single Action Army, they changed to steel and didn't look back.