Question

would it have been possible for speakers of indo-european languages to spread so widely without the aid of domesticated horses? explain in detail

Answer 1

No, the vast distances that existed between civilizations and the physical terrain (mountainous) that separated them were too great for humans to cross.  Journeys and trade routes would have taken years to cross.  Horses shortened these travels times and made journeys more survivable, as such the people were able to expand.