The Ice Caves offer a new avenue of non-subterranean dungeon-crawling. With the typical avenues of sculpted tunnels, chambers, and slick flows, the danger of an unseen pool is all the great. Even away from the wind, the PCs are constantly exposed to cold, making spending the night, resting to regain spells, and other options far from preferrable.
What is different?
The biggest difference in an ice cave dive is the presentation of the setting itself. Rather than massive weight of dark stone, the ice itself can be as clear as glass, or milky opaque. The upper caves could have their own illumination from light filtered through the walls. Some ice loving creatures could have even crafted the walls, and supports to channel light in such a manner. The color palette is going to be predominantly white and blue, becmong darker and darker blue until the light is lost due to snow cover, or simple depth.
Lifeforms in an ice cave are going to be radically different from those in a traditional stone dungeon. There is little food, no warmth, and not much biomass for fungus and such to break down. Consequently, the ice cave is going to be cleaner than a rock and stone cave. More things are likely to be frozen into the walls and floor than encountered, wandering about.
What is the Same?
The principle motion behind an ice cave is wind, drainage and temperature variation. Clear ice froze at a much lower temperature than milky ice, and milky ice will melt first. So a warm spell might cause veins of milky ice to melt, leaving behind the stronger clear ice. Combine this with ice sheets buckling, rolling, and otherwise acting like techtonic plates creates a suitable enviroment for an ice cave system. Salt water could also erode out ice caves, possibly making the entrances and such for the caves.
Why Use Ice?
Aside from simply changing the backdrop of a dungeon, the change from stone to ice removes many things that the tradition PC will take for granted. It removes all those special stone-work advantages of dwarves and elves, since ice isnt stone. It makes the PCs be more active, not letting them have time to lounge around, start a fire and rest, restore spells and HP by time. A fire could cause a roof collapse, resting too long invites hypothermia and frostbite. The PCs could even become lost in a funhouse like area of light refraction.
The Cold Path - Rather than crafting a complete ice dungeon, the entrance to a new underground warren/sunken ship/location has been covered by ice, and the passageway is somewhere beneath. Once the PCs trek through a mile or two of ice, they find the main entrance and welcoming embrace of the cold earth.
Ice Age - The McGuffin was lost in a north expedition/raid. The trail of the item was lost near a poorly known glacial area, and there are rumors of ice caves full of terrible spirits. The PCs investigate.
Shaken, not Stirred - The PCs are sent to find elemental ice, ice that will never melt. Supposedly it rests at the heart of the ice caves. Fun for parties or a greater evil?
Short, but added since the Arctic/tundra category had no entries. See Ice Age, the movie for a good ice cavern.