While the Reagan administration has turned a cold shoulder toward trade with the Soviet Union, the Agriculture Department recently proposed a rule change that would not only encourage horse-trading with Russia but also would make American billionaire and philanthropist Armand Hammer happy.

USDA's Animal and Plant Health Inspection Service wants to add the Russian Arabian Stud Book of Moscow to a list of "recognized breeds and books of records." That may not sound like much, but USDA recognition is expected to save Hammer and three of his partners at least $200,000 in import duties and make future horse-buying by the foursome less expensive.

Hammer, who heads Occidental Petroleum, and his partners in OPL Enterprises Inc. (Occidental-Petroleum-Lasma) asked USDA to recognize the Russian stud book after OPL purchased a purebred Russian Arabian stallion named Psnair from the Soviets for $1 million, which is not only a nice, round capitalist figure, but also the most ever paid in Russia for a horse.

The stallion's new owners hoped to bring Psnair into the country duty-free under regulations that allow purebred livestock free entry if the animals are to be used for breeding. The U.S. Customs Service, however, said there was no proof that Psnair was purebred because the Russian stud book, which records a horse's pedigree, never had been recognized by USDA. What's more, Customs said OPL would have to pay a 20 percent duty on the horse because Soviet Bloc countries do not have "most favored nation" trading status.

OPL quickly supplied USDA with a copy of the Russian stud book and got the prestigious Arabian Horse Registry of America to endorse its petition. USDA said the book meets acceptable standards. The USDA expects no more than six purebred Russian horses would be brought in duty-free per year. Comments on the proposed change will be accepted until June 21.