A good fence should be “horse high, bull strong, and pig tight.” These qualities became associated with a Texas fence, but they applied to any fence. The phrase dates from the 19th century.
19 October 1859, River Falls (WI) Journal, pg. 1:
“A Buncombe fence, Sir, is a fence that is bull strong, horse high and pig tight.”
1 December 1860, Ohio Cultivator, pg. 360:
...to fence stock out, fences must be horse high, bull strong, and pig tight;...
15 September 1866, Colman’s Rural World, pg. 276:
Last spring I procured a hook and an axe, and with a hand to help me, laid about three quarters of a mile down, and now it looks like a lawful fence, to-wit: “Pig-tight, bull-strong and horse high.”
31 August 1867, Prairie Farmer, pg. 133:
...and lines of beautiful hedges a mile long are not hard to find that are “horse high, pig tight and bull strong.”
21 January 1912, New York Times, pg. X4:
A Texas Court of Appeals has just rendered a decision defining what is a legal fence in the Lone Star State. It is that a legal fence must be at least five feet high and be of such construction that a hog may not go through it.
The requisites for a lawful and sufficient fence laid down by a Virginia Magistrate many years ago seems to fill the bill better than the judgment of the Texas court. Without specifying the material of which it was to be constructed, the requirements were that it should be “horse-high, pig-tight and bull-strong.” Any fence over which a horse could leap or a pig push through or a bull break down was not a lawful fence, and the fact that it had been so surmounted, penetrated, or broken down absolved the owner of the animals that has accomplished such invasions from blame or liability for loss.
11 June 1978. New York Times, pg. E1:
The house legislation was sponsored by Representative William S. Moorehead, Democrat of Pennsylvania, who likened it to “a good Texas fence—horse high, bull strong and pig tight.”