(Spoilers All) What happened to the sword and what happened to the horse?

I just finished reading the Samwell I chapter of ASOS, the one in which Sam slays the Other. Let's cut to the chase:

Before being killed by Sam, the Other pushes his sword through Small Paul, and as he is falling,

The weight of him tore the strange pale sword from the Other's grip.

Then Sam grabs the obsidian dagger, closes his eyes and charges the ice creature; pointy end in front of him.

When he opened his eyes the Other's armor was running down its legs in rivulets as pale blue blood hissed and steamed around the black dragonglass dagger in its throat. It reached down with two bone-white hands to pull out the knife, but where its fingers touched the obsidian they smoked.

Sam rolled onto his side, eyes wide as the Other shrank and puddled, dissolving away. In twenty heartbeats its flesh was gone, swirling away in a fine white mist. Beneath were bones like milkglass, pale and shiny, and they were melting too. Finally only the dagger remained, wreathing in steam as if it were alive and sweating.

Now, it's interesting to note the Other's sword was already separate from its owner when he was killed, but it seems to not be there after the creature melts.

After the adrenaline is down,

Grenn pulled Sam to his feet, checked Small Paul for a pulse and closed his eyes, then snatched up the dagger again.

A short dialogue ensues and the chapter ends. Keep in mind the dagger refered to is the obsidian dagger Sam used. There's no mention of the sword.

So it seems once you kill an Other, his armor and weapon also dissolve, no matter where it is -- unless you'd be more inclined to believe there's a certain radius it has to be in after its owner is killed. So Other-weaponry seems to be not an independent arsenal, but elements strongly connected to a specific wielder.

Now, more curiously, I would love to know what happens to the horse. The Other appears riding a horse, which he unsaddles from.

Sam felt a moment's relief, until he saw the horse. Hoarfrost covered it like a sheen of frozen sweat, and a nest of stiff black entrails dragged from its open belly. On its back was a rider pale as ice.

The Other slid gracefully from the saddle to stand upon the snow.

It never gets mentioned again. I feel that it would be an important piece of information: Are the riding animals also connected to their rider? Is the Other apart from these elements or a center of control for everything it uses?

The consequences to this are not that big, but I thought it was an interesting detail, because it means...

TL;DR: There's no looting an Other. If you want something he's using, you'd better keep him alive as well.