The first thing you can do to reduce the number of insects is to clean up around the barn. Manure attracts flies like a magnets, so mucking your horse's stall or paddock daily is a huge step in reducing barn flies. Another step is keeping the area dry, particularly in the evening. Don't keep water away from your horse, but empty buckets of dirty, stagnant water, and try to keep his living space as dry as possible. This can help prevent mosquitos. Mowing the grass can also prevent insects, mainly ticks, which hide in tall grass and can cause Lyme disease.
When getting rid of insects, it is also important to consider doing things that directly involve your horse. For example, a fly sheet and mask can go a long way to stopping flies and other insects from biting your horse or irritating their eyes. Fly spray can also be helpful, but remember that it usually wears off after a little while. Feed-through fly repellant is also becoming popular. Some feeds contain apple cider vinegar or garlic to prevent flies from swarming around your horse.
I make my own using essential oils, but regular fly sprays from your tack/feed store work as well. In the blend I use, I mix several insect-repelling oils with distilled water in a spritz bottle. Among these oils is a blend of citronella, well known for its insect repelling abilities as it is found in multiple bug sprays, lemongrass, rosemary, melaleuca, and myrtle. Other insect repelling oils include geranium, eucalyptus, cedarwood, and thyme. You do not need to use all of these oils in your spray; just a few drops each of an oil of your choice will do.
Insects can be annoying to have around, so making efforts to reduce them can be helpful. Even small things such as fly sheets can make your horse happier with all the bugs around.