As far as I know, there are no significant studies showing any sort of true effect whilst using essential oils in horses nor humans. My horse has COPD and I've had the best success preventing future episodes through dietary means and trying to minimize dust. The below website provides a good outline for COPD, including some suggested maintenance methods. https://equinemedsurg.com/pages/in-d...ne-heaves-copd
If your horse's diet is already balanced, then feeding certain supplements/ ingredients that could be beneficial in heaves. Two of them as already mentioned are vitamin E and Spirulina. You could also try supplements with anti-inflammatory effects, such as Omega 3. One thing to note is that technically, Omega 3 is neutral, but has an anti-inflammatory effect when Omega-6 isn't too high. Omega 6 is pro-inflammatory, which is needed but in a case such as Heaves, you do not want Omega-6 to get too high. MSM is another supplement that could help (10,000-20,000mg per day). You can also use something like Omega Alpha's Respirfree. I've used that occasionally in the past as needed, but you could also provide it daily.
Additionally, you should try and minimize dust or any other allergens. 24/7 turnout is usually recommended for this reason, rather than being in the barn. You could also steam or soak hay to reduce dust particles. For a while, I also refrained from brushing my horse indoors and instead would opt to do so outdoors. Shavings are also something you should look at as they can often induce flare ups as well. Also, free feeding from a round bale can cause flare ups since they are in a position to breathe in spores.
You should also have medication on hand in case he does flare up. I'm personally not an advocate for going straight to long-term steroids as this can create reliance on the medication; however, you can also do lots of damage by not medicating during a bad flare up. During a bad respiratory attack, the horse can scar and thus progress Heaves if the inflammation and immune system is not controlled soon enough. If you haven't already talked with your vet on which steroid would be best to use, then I'd encourage you to do so. Aerosols are also something good to have on hand.
Lastly, know that if you will see improvement, it can take a long time. I was curious and decided to take at least weekly respiration values over the seasons to see when my horse was more likely to have trouble. My horse has had COPD for about 6 years. He developed it at one barn and I did not see any amount of improvement until I moved him to another barn where there was better hay (square bales vs round bales) and 24/7 turnout. Even then, the improvement was minuscule. His average respiration was in the 20s-30s some days and he had a number of COPD attacks where we had to quickly intervene. It took about 1.5-2 years to see another change (average respiration then around 16-18 breaths per min) and fewer COPD attacks. We then moved him to another barn where the environment wasn't as ideal. He coughed a bit more in the morning, but was still better than before. I decided to move back to the previous barn after another two years and his breathing has been in the normal range since then. His last COPD attack was about 2 years ago and no medication has been used except during the COPD attacks.