Anne was born on March 1, 1913 in New York City into a wealthy family. Anne is behind one of the most extensive horse-related collections in the world. She began her collection at age six when she nailed up a bit and broken stirrup in an empty box stall in the barn. She continued to collect all through her youth and took her collection with her throughout her travels and marriages. The collection finally found a permanent home in the Museum of the Horse in Patagonia, Arizona. In 1957, she received a train carload of family heirlooms and shortly after she opened her museum. The museum featured her family heirlooms along with what she had collected throughout her life. Anne loved to attend auctions and continued to buy objects for her museum and collection. In 1989, her husband, Floyd, died and Anne came into poor health herself and she knew that she had to find a new home for her museum. That home would later be the Museum of the Horse (now the Hubbard Museum of the American West) in Ruidoso Downs, New Mexico.

The Museum of the Horse (now Hubbard Museum of the American West) was founded in 1989 as the Hubbard Museum, a Texas non-profit corporation. The museum was originally created so that it could handle the extensive personal art collection of Museum founders, R.D. and Joan Dale Hubbard. In 1989, Anne Stradling contacted the Hubbards and asked them if they would be willing to take her collection and give it a permanent home. Stradling asked that the museum be located near the racetrack and the Hubbards bought the old Chaparral Convention Center and renovated it to become the Museum of the Horse. The Museum first opened its doors in May of 1992.

In 2005, the Hubbards gifted the museum to the City of Ruidoso Downs. When the museum was transferred to the city, the name was changed to the Hubbard Museum of the American West. Today, the museum is still owned and operated by the City of Ruidoso Downs.