There was no distillation in the pre-columbian Americas. Distillation itself was relatively new in Europe at the time, having only been introduced a few centuries early and really only having spread through Europe in the about the century prior to Cortes' expedition, and then primarily as an alchemical/medicinal ingredient. Rum distilleries wouldn't show up in the Caribbean until about a century after Cortes.

The drink of the Spanish was, quite firmly, wine. To the point that enormous amounts of it were imported from Spain to supplement the early efforts to plant vineyards in Mexico. One early plan to drain Lake Texcoco, for instance, was incredibly unpopular in part because it was funded by a tax on imported wine.