Probably, if you humanely euthanize the horse first.
The fabricate spell calls for “raw materials”. A living horse is not raw materials. The spell description states:
Creatures or magic items can't be created or transmuted by this spell.
So while the horse is alive, it is a creature, and cannot be transmuted by the spell.
However, there is a strong case to be made that a horse corpse is an object, not a creature. If the DM rules that corpses are objects and not creatures, then fabricate should work just fine. That linked Q&A also contains some good arguments that a creature’s corpse still counts as a creature, so you will have to ask the DM. It is worth mentioning that lead rules designer, Jeremy Crawford, gave his personal but unofficial ruling on Twitter:
A non-undead corpse isn't considered a creature. It's effectively an object
We can also look to standard industrial usage of the phrase "raw materials" for some insight, since D&D 5e generally uses the standard English meaning of words unless otherwise noted. The United States Department of Agriculture Food Safety Inspection Service considers animal carcasses and parts of carcasses to be "raw materials". For example, 9 CFR § 318.6.(b).(4) states:
Detached spinal cords from cattle 30 months of age and older shall not be used as raw materials for edible rendering.
Again, I must emphasize, the horse should be euthanized humanely. Alternatively, I recommend just purchasing a Burger on the Go device, from inventor Dwight K. Schrute:
I invented a device, called Burger on the Go. It allows you to obtain six regular sized hamburgers, or twelve sliders, from a horse without killing the animal. George Foreman is still considering it, Sharper Image is still considering it, SkyMall is still considering it, Hammacher Schlemmer is still considering it.