The most important nutritional concern when hauling horses, both in the trailer and at an event, is dehydration. Try to haul your horse in the early morning or late evening to avoid water loss by sweating while in the trailer. Next, make sure water is available. Experiment with different options to encourage your horse to drink, including flavoring your horse's water with sugar-free gelatin or adding a small amount of feed to the water. It is important to experiment with this flavoring while at home before you get on the road. Make sure water is always available and if your horse is not drinking, stop and unload to allow drinking. Dehydration can lead to colic as well as respiratory disease, so it is critical to prevent dehydration if possible.
Another concern is changing diet. You never want to abruptly change a horse's diet especially before or during hauling or at a show. Always take your feed to the show and for use on the road and don't take a chance on changing feed as colic is likely to develop. The folks at Kentucky Equine Research recommend adding a probiotic to your horse's diet when traveling and this is probably a good idea as it is certainly not harmful. However, make sure you start this supplement at home before hauling and don't just add it just when you start hauling as that would be similar to a change in feed.
Lastly, it is probably not a good idea to give medications to horses immediately before hauling as it will be difficult to observe a reaction. And if your horse needs medication, consult your veterinarian to see if it is recommended to give the specific medication during traveling.