It is worth getting the horse trained to accept spray bottles... but, you can use one of those fuzzy-outside-plastic-inside applicator mitts or homemade equivalent if you want, but 
DO NOT GET THE HORSE AT ALL 'WET' WITH THE REPELLANT. (For this reason, a sponge would be unwise). 
Wetting the skin, which is to say wetting the hair to the point that it looks wet, can produce really bad skin reactions. Actually I've also seen a horse with colic and neurological symptoms from being wetted all over with flyspray, although nearly nobody is dumb enough to do *that* 
		
		
	
	
 (He recovered, but it was a bit iffy for a while, and he was not rideable for several weeks)
Our main problem here, unfortunately, is mosquitos and some blackflies... and truly the only spray that I have found to help is water-based citronella-smelling 'cheap' sprays like Bronco, applied EVERY AFTERNOON before dusk. (The pricier ones, like the red or black-label Absorbine fly sprays, work just about as well for the first 12 hrs, but no matter what the label says, they just DON'T repel mosquitos for longer than that, and IMO it is just not safe or intelligent to flout the label instructions by applying them every single day; whereas you can safely do that with the cheap water-based ones)
A fly sheet and fly mask help a lot. Also, if there is somewhere protected you can rig it, a strong barn-type fan that the horse(s) can stand in front of.
Good luck,
Pat