Here's an idea. This is sort of inspired by the Sonic movie, the one with Hyper Metal Sonic in it. (I think it's called Sonic OVA.)
After the snowy mountain, the character falls through a platform of thin ice, leading them underground. These caves are filled with both ice and lava.
"The lava flows through the ice like blood vessels." ...Or something like that.
Perhaps Eggman had built a base under the mountain, powered by the heat of the lava. This then can lead the characters to a room with a space rocket. (All Sonic games MUST end with a space level. ;) )