Like, if I have matching set from the light armor tree and am wearing studded armor but hide everything else, will it apply that perk?

That's a good question and I've wondered the same thing myself. I think it may fit in with hide armor, but I'm not certain since it's in a category of its own when you smith it at a forge.

I don't think they're in the same set, to upgrade hide you use Leather and to upgrade studded you use an Iron ingot.

Actually, I just tested, and it is. I COC'd to Whiterun from the Main Menu, then added Studded Armor, Hide Boots, Hide Bracers, and a Hide Helmet to my inventory. Finally, I pumped my Light Armor skill to 100. With 5 ranks of Agile Defender and the Custom Fit perk, I had 152 Armor Rating. After taking the Matching Set perk, my Armor Rating jumped to 190. So the Studded Armor is considered to be part of the Hide Armor set.

yes, studded armor have armormaterialhide keyword so it will benefit from matching set perk with hide bracers, boots and helmet also remember studded only has armor no boots and bracers so it is meant to be combined with hide bracers and boots