Welcome to the forum! Whew - that is going to be a tall order! Going on a horse, almost by definition has to be portable. So outside of cardboard and some sort of fire garland, seems like you'd be in the market for something battery powered?

Strands of LED lights would be the go-to there, just for the energy efficiency. If you want plug-n-play, I'd search for 'fairy lights' which typically have a battery pack built in...3 AA cells and you're off to the races!

A step up from there would be a strand of neopixels that you could program to twinkle red/orange/yellow and look like fire.

Further still, search for 'faux fire' on here, or browse through the Technological Terror section. Some good discussions on using ultrasonic mist makers and shining LED lights through for more fire effect... They run on 24V which is within the realm of batteries, though keeping all that sloshing water relatively contained on a horse might present more of an issue.

The high end would be some sort of fog machine, but those are usually mains voltage...120VAC in the states, so a little harder to run on batteries. But as I am often told, where there is a whip, there is a way... so even that could be made to work with effort!

Hope this helps.

 

I would say you best bet would be to grab a few solar-powered flame lamps. They would be a bit bulky on a saddle, but the flame effect is pretty good and they are self contained.

 

I once did a fire ball prop for the wicked witch of the west to throw at the scarecrow for a stage play of Wizard of Oz. I used those tiny wire battery LED strands in Yellow and red and wove them in some orange red and yellow netting fabric and tied a ball of fabric around the battery pack into one end and had the LEDs and fabric coming out like a comet tail. Some pictures of what Type of items I used.

 

Interesting design Batbuddy! Do you have any pics of the finished fireball?

 

Unfortunately no...

 

There is also the method where you point a fan upward beneath the actors hands and they wear gloves covered in ribbons of flame-colored fabric.

 

It's wicked old-school but if the horse is going to be in motion / there is access to moving air, I've had success with the old "flaming cauldron" trick - - you could rig up some orange / red /yellow battery operated LED's, make some "flames" out of a chiffon-like fabric, and bob's yer uncle.
I did mine in a fire-pit that had a box fan hidden in the firepit, with the "flames" attached to the plastic grate of the fan.

Link below is to the quick example on Amazon:

Amazon.com: 3D Fake Fire Light, Hanging Flame Light, Artificial LED Silk Flame Stage Effect Light Realistic Campfire Lamp Prop Flame Light for Halloween, Festival, Party, Night Club, Theater Effects : Musical Instruments

Buy 3D Fake Fire Light, Hanging Flame Light, Artificial LED Silk Flame Stage Effect Light Realistic Campfire Lamp Prop Flame Light for Halloween, Festival, Party, Night Club, Theater Effects: Flame Effects - Amazon.com ✓ FREE DELIVERY possible on eligible purchases

www.amazon.com