Price was riding in a 4x4 vehicle with her boyfriend Leandro Penna when a pair of stallions jumped a fence and galloped into their path on a remote country road in Argentina.
The horses were killed while Price and Penna, who was behind the wheel, both suffered severe whiplash and cuts.
The former glamour model, who is an avid horse rider, insists she is devastated by the accident and ""lucky"" to have survived.
Price tells Britain's Daily Mirror, ""It was absolutely terrifying. It all happened in a flash and I have absolutely no idea how I wasn't badly injured.
""I feel so lucky, but more than anything, I'm just distraught about the horses. It was so upsetting.""
Price has been dating Penna since February (11) and was visiting his native Argentina to meet his parents, Mercedes and Hector.