How the fuck does Gregor Clegane not kill horses with the sheer weight of his giant, armored arse?!
So, Gregor is said to weigh 190 kg. (420 lb.)
A quick Google search tells me plate armor weighs around 30-35 kg. (66-77 lb.)
Gregor's armor is said to be the thickest and heaviest armor in the Seven Kingdoms, and that no ordinary man would be able to move in it! Therefore Gregor's armor must weigh a lot more than the average armor! Lets just be lazy say his armor weighs double that! (He's a big, strong boy, after all)
We will then end up with 60 kg. (132 lb.) worth of armor.
An armour Gregor would then be 250 kg! (551 lb!)
Playing around with a horse carry-weight calculator, I got to the results that a horse weighing 1270 kg. (2800 lb.) would be able to handle a rider weighing 254 kg. (559 lb.)
Another quick Google search says that the biggest horse, the shire horse (an absolutely gorgeous boi) in average weight between 816-1086 kg. (1800-2400 lb.) That would make their carry weigh to be between 162-216 kg. (358-477 lb.)
In conclusion, Gregor can indeed ride a shire horse Lady Godiva style (okay, he can probably wear clothes too), but even if we say his armor just weighs 30 kg. (66 lb.) He'd still be a just a little too heavy for the poor creature... though I doubt he cares. We do hear descriptions of how silly he looks mounted, as his horse looks like a pony under him!
But Gregor should value his horses more, for it can't be easy finding one strong enough for him! Though of course he lives in fantasy universe, so maybe it's not actually that difficult.