Green’s Dictionary of Slang

of a horse, stolen and smuggled from Mexico.

1926		D. Branch Cowboy and His Interpreters 35: ‘Shanghai’ was one of the many cattlemen that traded occasionally in ‘wet ponies.’.
1929		J.F. Dobie A Vaquero of the Brush Country 81: The code of these ranchers [...] forbade stealing from a neighbor, but it generally permitted trading in ‘wet’ horses – horses stolen in Mexico and smuggled across the Rio Grande.
1944		R.F. Adams Western Words (1968) 176/1: wet stock. Cattle or horses which had been smuggled from across the Rio Grande River after having been stolen from their rightful owners in Mexico or Texas. Later the term was used to refer to any stolen stock [DA].