If your reaction to that question is like mine, you will be muttering “There’s no such thing as ‘Indo-Europeans’—Proto-Indo-European is a reconstructed language with a few clear features and lots of hypotheses, and barring the development of a time machine we’ll never know who spoke it.” But many people are unhappy with that degree of skepticism, so there will probably always be attempts to pose and answer the question. The latest is The Horse, the Wheel, and Language: How Bronze-Age Riders from the Eurasian Steppes Shaped the Modern World by David W. Anthony; the NY Times review is by Christine Kenneally (author of The First Word, a book that attempts to answer another unanswerable question, how language began), and you can read the first chapter here. As Kenneally says:
The impact of horses on the reach of language is particularly important to Anthony, and he conveys his excitement at working out whether ancient horses wore bits (and were therefore ridden by Proto-Indo-Europeans) by comparing their teeth to those of modern domesticated and wild horses. He muses on the “deep-rooted, intransigent traditions of opposition” that existed along the Ural River frontier, slowing the spread of herding and the cultural innovations that went with it.
If the idea of using primeval horses to illuminate protolanguages excites you, you will probably want to read the book. If you find it (and similar speculation about “a world in which spoken poetry was the only medium”) too hypothetical to take seriously, at least it allows the mind to roam freely over the ancient steppes, snorting and whinnying and heading wherever its fancy takes it, trampling underfoot the captious questions of carping quidnuncs.