Yes, I don't think it was bar material, but sole growing a bit weirdly, a lot of which grows out of the bar laminae. I think when bars become overgrown, this is what can result, perhaps as Gotta describes. Interesting that IME you only tend to see this in heavy breeds. Interesting you mention it could be a breed trait with Haffies & frog material. I haven't worked on a Haffy for a long time & don't find this with other heavy breeds(reg work on clydies, freisians & perchs), but they do tend to put out extra sole, which IME needs trimming more than light breeds... excuding donkeys & minis who also tend to need sole maintenance.
But essentially I don't think it matters much where it comes from, not saying I'd treat it any different than you did. I think the proof's in the pudding when you talk of finding crumbly sole beneath the hard stuff. Also that it didn't just 'pop back' when you removed it, which IMO indicates you probably should have left it
Frogs can be notoriously hard to trim sometimes. They can get almost as hard as wall material but their flexibility means they still yield to the knife without being cut easily. Yes, you can use the nippers if possible, if you're very careful, but using a knife in a sawing action works better than just trying to push it through, as you would wall or sole.
I don't think you need to get 'aggressive' with the frog at all really, just remove the dags & flaps, and keep those heels down. Horses do tend to grow 'layer upon layer' of frog material when it's trying to reach the ground(if it's not rotted away) & I think his frogs would be flatter & more whole looking if they were in better contact with the ground - and firm ground, if deep sand is all he gets, I'd endeavor to work on firm ground & provide some if poss in his living environ.