Yeah, but I also meant the typing. Not only would they be similar, they would be also both fire. That is why I don't think we will ever see another fire horse. However, they could make it other element (after all we did get donkey inspired ground type in gen7 right? And we also have different element based cats and dogs).
Gen1: Lets make a dog! Make it Fire-type! And so Growlithe was born.
Gen2: Lets make a dog! Make it Fire-type! And thus Houndour was born.
Ohh! But Houndour is a Dark-type as well! Indeed it is, but the point still stands. Ponyta and Rapidash are classical pokémon designs, heck, if they were made today, they'd probably be Fire/Normal-types. So giving this hypothetical Fire-horse an added typing would drastically change how it could function aside from Rapidash.
-horse could work and would have a vastly different movepool to Rapidash and would be more akin to Mudsdale then Rapidash. Hopefully not that slow, but an armored horse would be wickedly unexpected. It would probably still share moves like Flame Charge, Flare Blitz, Drill Run and High Horsepower, but it could get access to a lot of cool Steel-type moves as well: Some new high-power Steel-type signature move to do with jousting and having bolted on lance. Moves like Knock Off and Fell Stinger, along with Jousting Blitz (high powered Steel-type move akin to Flare Blitz) and Flame Charge could make for a cool moveset that would let it work completely different than Rapidash (Fell Stinger would mean that Flame Charge would do respectable damage to compensate for the low starting damage, while Flame Charge would compensate for the high odds that a Fire/Steel-type probably won't be as fast as desired). Maybe something like just do Flare Blitz and make a Steel-type Flame Charge (Flash Charge?) so that the primary STAB at least has the high damage output, while the secondary STAB gets the extra benefits.
This is all pretty cool, but it clashes with my dream for a Grass/Steel Velociraptor Starter.