"See a man about a horse" is an idiomatic expression that implies going to attend to an urgent or important matter, often one that cannot be disclosed to the public. There are several other phrases that convey a similar meaning. For instance, some people may say that they need to attend to some "personal business" or "take care of some important matters." Others may simply state that they need to "step out" or "run an errand." For those who enjoy puns, one could say that they need to "tack-le" a matter or "gallop" away to attend to something important. No matter what phrase one uses, the meaning is clear - they need to attend to something important and cannot be delayed.