May not be able to get you an exact date (hard to do without the labels), but if you had a photo of the "neck" of the bottle, and any lettering on the bottom or side of the bottle, we could easily get you an approximate date.
White Horse bottles did not change much over the last 70 years, but there were some small changes to the "neck" as the company changed from Cork-driven closures in about 1920 to Metal Screw-caps (c.1922) & Spring-cap (1929) closures, and back to Plastic Screw-caps in 1963. (Your description of the metal cap sound like a Spring-cap design, which was used from 1929-1963).
Additionally, there were several changes to the way the contents were measured over the years, particularly in the 1930's, 1950's, 1970's.
If the bottle was produced between 1934 & 1967 is may also read: "Federal Law Forbids the Re**** or Reuse of this bottle" on the top of the back side.
And there may be a disclaimer about being the exporter at the bottom of the back side.
Walter C Hurst