The show, being held at the Will Rogers Memorial Center in Fort Worth, will continue through to its scheduled conclusion on Saturday.
Show officials are working on a revised schedule to accommodate the activities that were postponed.
"Obviously, we are delighted with the results," said club chief executive Steve Taylor.
"We are especially proud of the co-operation between the show officials, the Will Rogers Memorial Center representatives and the others involved in the decision to implement the precautionary measures."
Taylor said he was grateful for the patience and co-operation of exhibitors who supported the precautionary measures.
Voluntary quarantine protocols were initiated on Tuesday night after the horse displayed what appeared to be neurological symptoms.
Center staff immediately began the precautionary quarantine protocols, including isolation of the horse in question and two other horses that arrived at the show in the same trailer, as well as regular sanitisation of the barn and implements.
Assistant facilities and public events director Kevin Kemp said center staff are prepared for such situations and are ready to respond.
"The good news for everyone involved is the tests came back negative," Kemp said.
"In cases like this, we have a number of protocols in place that help us ensure the health and safety of the show participants.
"These are part of our efforts to be prepared and provide the best and most complete service possible to the show participants who come to our facility. Our staff acted immediately, and because of that we were able to reduce the risk."