The real question is a practical one, rather than a legal one. We all live and die on our reputations. For an online business do you really want people who are already connected to the internet to tell their friends to never come to your events, to find a blog somewhere to complain about you, to make their own blog about how rotten you are for canceling/postponing the event and not giving them (apparently) anything, like a ticket to the next event (maybe two because of the inconvenience that you have cause them). Then they could also file suit against you. Believe me, the cost of the refund will pale in comparison to the time, effort and money that the lawsuit will cost you. You didn't mention whether the event was a "consumer" event subject to Ohio's very powerful and almost punitive consumer laws. It's possible that a court could force you to pay the up to three times the money back, plus attorneys fees (THEIR attorney's fees, don't forget about paying your own).
If I plan to go to an event, I block out the time for the event. If the event is then postponed, I may not be able to attend because I already have something else scheduled. Why should you get to keep my money when I originally gave it to you only because you were doing what I wanted to attend on a date I COULD attend.
Why don't you give refunds? Because they have potentially taken someone else's seat in a live event (if it's an online program there is little chance of that)? My suggestion would be to re-write your refund policy to allow them some flexibility and to take the risk out of dealing with you. Common refund programs that I have seen are Full Refund if canceled prior to 2 weeks (or some other reasonable time) before the event, Full Credit for a same priced later event if after the "2 week" deadline, but prior to the event, no refund after the event, and then be flexible when they call and say, but I couldn't attend at the last minute because (what ever outlandish "dog ate my homework" excuse they have for you). So give them a pass to a later event, they end up loving you and telling others about you, giving you higher sales for free. This is for when THEY want to cancel. When YOU cancel or postpone (same as canceling to them if they can't or don't want to attend on the new date), why would you EVER consider not refunding people their money, because, of course YOU CANCELED!
You have inconvenienced them. Do whatever it takes to make it right. Yes, offer them their money back, maybe even before they ask. Given them the choice of either the refund or 2 tickets to future events. Forget what technicality there might be in the law or your "contract" (website). Do for them what you would like to have done if someone else did the same thing to you.
Answered on Oct 16th, 2012 at 3:09 PM