So, what are Ice-types, really?
The Purpose of the Ice Type:
Purpose of Ice-type is relatively simple, assist Water, replace Water late-game and defeat Dragons. Sounds simple, but it is actually quite complicated. For example, two of the types Ice is weak towards to, Fire and Rock, are defeated by Water. Water also has several nifty quad offensive strengths, against Rock/Ground, Fire/Ground and Fire/Rock, types Ice cannot defeat after Fire gained resistance to Ice. Assisting Water is also a crapshoot, since Water is far too versatile to be locked into a single support type, though Ice helps Water being so powerful. Defeating Dragons is also a crapshoot, since Dragons have Steel, Fairy and other Dragons to deal with. Ice is just the most reliable of all.
So, what is left for Ice then? Well, nothing really. While Ice generally finds a way to become relevant due to appearing in odd places, it never finds itself relevant. Ice's original purpose was to become the "Cannon" of all types, which by nature required some bulk and weak offense to balance things, these days it is the "Glass Cannon" type, a status that fits Ice-type very well, but does not fit the bulky arctic Ice-type Pokémon. As Wulfric says, either Ice-type beats you, or it fails. There is no in-between. Well, okay, Alolan Sandslash and Ninetales, Kyurem and Water/Ice try to fit that role, but they are not particularly successful.
Ice-type is really, really bad.
The Aesthetic Archetypes of Ice Types:
Ice-types can be generally categorized into three major groups, organic, frozen and inorganic. In terms of colors, they can be generally light blue or light white color. Their aesthetic archetypes can be divided as such:
Generally white colored and furry, these are generally thick coated and fat Pokémon, they generally reside in Field and Monster groups. They have some affinity for Normal, Ground and Rock-types.
Generally based on more migratory species, these are Ice-types that do not reside in cold regions. They have some affinity with Water.
Basically variations of ice, they can appear as icicles, ice crystals, glaciers and whathaveyou. They have some affinity with Steel and Electric.
Generally organic species that are frozen, though inorganic members also exists, these are species that are Ice-type because they have frozen parts around them.
The In-game Archetypes of Ice Types:
There is only one in-game archetype, and that is late-game Ice-type. Everything else are either too few to belong to archetype, or have some other gimmick.
The Stat Archetypes for Ice-types:
The Tank The conventional tank we all know and love. In Ice's case, tanks are generally focused on one single offense and defense, generally the same one.
The Balanced: The conventional balanced we all know and love. In Ice's case, there is generally no stat that is truly superior to others in these Pokémon.
The Glass Cannon: Not to be confused with the conventional meaning of the name, Ice-type Glass Cannons are bulky and slow, but they are still focused on offense over everything else like the regular Glass Cannon.
The Glass Wall: Ice-type's variation of the conventional the wall, the glass wall is generally a slow defensive Pokémon that excels in one defense and tends to have useful offense, but absolutely pathetic in the other defense.
The Glass Speeder: Ice-type's variation on Water-type's Speeder, Ice-type Sweepers tend to be more annoyers or wall breakers than true sweepers. They might have okayish bulk in one area, but they will either laughable offense or defense in another.
All Ice-types have relatively balanced stats except one or two stats that serves as their Achilles' Heel, somewhat mimicking Electric and Water but they are more easy to break.