The history of horse domestication, according to recent research, starts somewhere on the plains of eastern Europe 6,000 years ago. Since then, cavalry had become a major turning point in Old World history more than once. For further history on the specifics, look to this site.
But in an alternate history scenario, men tamed horses when the majority of Europe was either buried in ice or a dry sea of mammoth steppe. Let's say that the horse got domesticated three times earlier than in OTL. Using the technology of the time, would it be possible to tame horses at the height of the Last Ice Age?