What did the prize list (omnibus listing) say about refunds in case of cancellation. If it said “no refunds in case of cancellation” you are out of luck.
Typically you must apply IN WRITING for a refund. Did you do that, or did you just assume you would get a refund?
If the prize list said you could get a refund, I THINK they have until 30 days after the scheduled date of the competition (rather than the date of the cancellation notice) to give you the refund.
If the prize list said you would get a refund, AND you requested it in writing, AND it is more than 30 days after the competition date, you can/should complain to USEF (USEA has nothing to do with this part of the process, though they might give you a “shoulder to cry on”).
A good many years ago, a Horse Trials (in Texas I think) was already in a poor financial condition, and had to cancel because of a major weather problem. Their omnibus listing said they would give a refund in case of cancellation. But they had already spent all the money, and couldn’t/didn’t make any refunds.
The USEF hit them with a MAJOR penalty (which they were not able to pay AFAIK). Nobody actually got refund, but it certainly led to the permanent cancellation of that Horse Trial.
So, if you are getting the runaround, you could certainly tell them that you indent to contact the USEF about non payment of the refund.
(Mind like a sieve!)