Horses are normally excited and fresh when they go to new places, before thinking that his anxiety isn't simply a way to demonstrate he is happy or afraid of being in a new place I would consider: the age of the horse, his experience, how many shows or new places has he been, hoe long have you been riding him and how strong does he trust you.
If the answers to these questions show that he is young and you have few experiences together then I would consider it as normal, he needs to get used to going to new places and to be at shows, if instead its quite a few years that you are traveling then I would ask yourself are you calm or anxious when you go at shows??
As a rider you have the ability to transfer to your horse your thoughts and emotions so if you are anxious so he will become and if he is anxious and you are calm you can transfer him your emotions of calm and relaxation.
You can remain calm by working on your emotional state by managing:
A) your physiology
to influence your emotions
B) your mental focus
be aware on what you concentrate on, if you are nervous because you are tense due to the show you will transfer your feeling to your horse. Pay attention to:
1) your inner dialogue - what you tell to yourself becomes your reality
2) Language - the word you use influences your emotions
3) questions - the kind of questions you make yourself influence your emotional state
Concentrate in remaining calm when you go to new places and horses, ride, think and act as if you where at home and transfer to you horse a great sense of trust and he will start to follow you...