Much like smelting ore gives you ingots, is it at all possible to 'deconstruct' clothing and armour to get the material(s) from them in Skyrim?
Not in the original game. There are several mods that let you melt down weapons, armor, etc. such as this one. Up to you to decide if you want to play with a third party mod. If you haven't tried mods yet, make sure to backup your saves before doing so!
I haven't had any mod break my saves yet, but I have had warnings in the game about "objects no longer available" and such. As mods can add new objects and entities in the game world, it can potentially create a save that you won't be able to load after removing the mods. So keep that in mind.
You can disenchant them to learn their enchants. This destroys the item and makes you able to cast the enchant that was on the item.
But you can't destroy an item in order to get back the base materials. Once an item is made the base materials are gone forever.