It was a caustic solution, high pH. Similar to debudding paste. Back in the day, before freeze branding, caustic branding was called cold iron branding.I never used it or saw it used but once, as it was still taught in Vocational Agriculture in the late 60s when I took the courses as a teenager. It was a relatively thin liquid you mixed. From what I do remember, it was mixed with a petroleum solvent (they recommended 'coal oil or kerosene' about 10:1 kerosene to caustic, then thickened it with cornstarch or even fine sawdust to make the paste.
From an old book I have (date on it says 1946)
"Branding.—All brands and marks must be approved and recorded by the Livestock Identification Service, California State Department of Agriculture, Sacramento. To avoid unnecessary damage to hides and to the animals, brands should be as small as is consistent with ease of identification. Since the brand increases in area with growth of the cattle, small brands may be used if the calves are only a few months old. Hot-iron branding is most commonly employed and, in general, is most satisfactory. Cold-iron branding, by using a caustic fluid, causes very little pain and, when carefully applied, makes a permanent brand in the skin. Since it does not change the direction of hair growth as does the hot iron, it becomes illegible when the hair grows out. Caustic branding fluid is therefore not recommended for general range use."