No, run deeper into the cave.

"Umm, no" You get up and kick his legs out from under him, before running deeper into the cave.

"You eijit! Yer gonna freeze!" Grinko yells from the floor. You keep running, down into the depths of the cave, until you come across a crossroads, illuminated by a faint fungoid glow. You stop, and consider your options.

The left path seems warmer than the others, but knowing this mountain's reputation, that means either dragons, demons, lava, or two or more of those.

There's ominous chanting in some unrecognizable tongue coming from the right passage, which means something intelligent is down there, but they might not be friendly.

Straight ahead leads only to blackness.

Or you could head back up to the surface. It's probably daylight by now, and Grinko's probably gone.