Well sucking farts out of dead horse is actually very useful. It brings down the bloated belly so you don't have to dig as big of a hole to bury it. Not a fun job but saves time!
There's a device that looks like a hollow awl which is used to relieve a bloated cow (or horse).
But for large dead animals it's just easier to dig the hole (you'll need an excavator unless you're addicted to very hard labour), put in a layer of wood chips or scrub stuff, next shove in the dearly departed, pile on more fuel, pour on much accelerant, and burn all in the hole. Stand up-wind and drink beer until the flames are well down. Then shove over the dirt.
If it was a good horse (and most are far better than their owners), a Viking sort of wake during the fire may be appropriate - music and whatnot.
Forget those who have no honor for anything except their own bellies. They deserve oblivion and no markers.