Given that I'm only starting A Clash of Kings and haven't yet seen past season 5 of they show there is plenty I haven't encountered yet, although I am curious...
According to the source in this answerthis answer to What is so special about Valyrian steel?What is so special about Valyrian steel?:
"Valyrian steel blades are lighter, stronger, and sharper than even the best castle-forged steel".
Obviously lighter and stronger armor is something you want too (sharp, probably less so, but you wouldn't need to sharpen the steel for armor..). I do not recall any character so far directly mentioning or owning Valyrian armor, but are there any records of it ever existing (even in Valyria, pre-Doom)?
If not, are there reasons for it not existing? It seems like a good idea in theory to use a lighter and stronger armor with a lighter, stronger, and sharper weapon.