There are mixed things to point out when speaking of Ice types. For one, a lot of their type weaknesses are rarely used. Another thing is that there are only two Ice types that are actually weak to Fire type attacks: Jynx and Articuno (The remaining Ice types are all half Water types, and are therefore neutral to Fire type attacks). However, those two can deal with Fire types in their own ways. With that in mind, it's easy to see that Ice types are extremely useful, in theory. Certain Ice/Water types are not as useful when looked as serving a team's purpose of a designated Water type, so some can be disregarded altogether. Other than that, there are three specific Pokémon that advocate what a good Ice type should be like, and they are: Articuno, Jynx, and Lapras. Not only are they strong on the stat department, but their usefulness is extremely high and they can be quite versatile in battle. In Lapras's case, you've got high TM compatability and high stats. In Jynx's case, you've got high speed and special, and a good mix of TM and natural skills. Ice attacks themselves are incredibly strong. They have the incredibly painful side-effect of leaving a Pokémon with FRZ status (if you're lucky enough), which totally immobilizes the monster affected. A frozen Pokémon can do nothing except wait for itself to faint, or it can hope to be thawed out by a wayward trainer who is dumb enough to use a Fire attack on it.
Ice types are resistent only to Ice type attacks.
Ice types are weak to: Fire, Rock, and Fighting type attacks.
Ice attacks are ineffective versus: Ice and Water types.
Ice attacks are strong versus: Flying, Grass, Ground, and Dragon types.
Articuno's got high HP, high defense and special, and has decent attack and speed ratings. Other than that, TM selection is not that great, but it's enough for Articuno to work well with. Blizzard and Ice Beam get STAB, so use whichever you feel like using. Double-Edge doesn't really work off of a high attack stat, so you might want to use Substitute and Sky Attack together. Articuno can Double Rest relatively well, so once that is set up, fire away with some STABBed attacks. A good Ice type all around, but not nearly as versatile as Lapras. His major threats are Electric attacks. While Rock Slide does spell disaster for Articuno, the most common users of that attack are part Ground-type, and are therefore weak to Ice. For Articuno, if you want assured success, just go for the mega-defensive mode. You will be a little short in the attacking department if you decide to go with DT, Rest, and Substitute, but the latter of those three skills is not completely necessary; you can put Fly or Sky Attack or Double-Edge in there.
At first glance, Cloyster's stats seem to be somewhat appealing; highest defense in the game, good special and attack ratings, and low speed and HP ratings. However, his weaknesses are predominantly special based, rather than physical based. While he is weak to Rock, no one in their right mind would bust out a Rhydon or Golem against this guy. Furthermore, hardly anyone uses Fighting types/attacks, so that case is argued. So, in other words, his high defense is an asset, but not a barricade which you can hide behind. He's got decent TM compatability, so make use of it. He can Explode, so make use of that. He gets STAB for two hard hitting attacks, which is always a plus. He learns Supersonic, so if you're feeling saucy, go for it. Generally, you might want to set up a Substitute to help you get in a hit. Or, you can attack on the turn the opponent switches instead of wasting HP on a Substitute. That philosophy works for all move sets. Cloyster can do damage, but there are stronger water types out there. Make your choice carefully.
Wow.... talk about a lost cause. Dewgong really has very little to offer. Low attack, mediocre defense, good special and HP, and low speed are his attributes. Make use of what STAB he has from using water and ice attacks. He learns a good slew of physical attacks, but his horrible attack doesn't make good enough use of them. The third move set I suggested for Dewgong attempts to make use of Dewgong's ability to learn Horn Drill. The key is, try to paralyze, then fire away with whatever you've got. The second move set, which utilizes Double Team and Rest, is not something I personally enjoy using, in fact I detest it. It is basically a last ditch effort to make something out of an already hopeless case. Good luck to whoever uses this guy.
Jynx is a dual Ice/Psychic type and is the fastest Pokémon out there that learns a decently accurate Sleep attack, Lovely Kiss. This makes her a good starter because she can get the jump on other opposing sleep-starters, all of whom she is faster than (bar Gengar, who is a rarity). The only problem you'd run into when starting the match with Jynx is of course, another Jynx, or hard-hitting starters such as Tauros. I've had a bad history in the luck department when using Jynx, so I've let her go and have gone with Venomoth instead. Other than that, Jynx has somewhat low HP, horrible attack, the lowest defense rating of a final stage Pokémon, and high speed and special. Her first move set is standard. Just put them to sleep. While that happens, you may want to put up a Substitute, Reflect, or even Double Team up. Then, you just blast away with her STAB-induced, hard-hitting Psychic and Blizzard attacks. The second move set is more laxed, I suppose. Sleep them, then slowly wear them down with Seismic Toss or something. Sub-up if necessary, and get in a few good hits with Ice Beam. If you're lucky, you'll freeze an opponent. Jynx is good, but I don't think so highly of her, mainly because luck screwed me over and I was let down by her. She's definitely useable.
While there are tons of move sets for Lapras, the first selection is most fundamental, and is the most commonly used move set. It all depends on the final move slot. Where I suggested Body Slam, you personally may choose Sing, Reflect, Substitute, whatever. There really are tons of choices that work. Body Slam is used often because paralysis, coupled with Confusion, can really annoy opponents. I don't, however, suggest Surf. You really don't need it. Blizzard or Ice Beam will get the job done and then some. The second move set just aims to pump up defensive levels. Put up Substitute or Reflect, and then Growl to piss physical attackers off. Blizzard and Thunderbolt are the main attacks. Lapras is one of the strongest water types out there, believe it or not. Lappy combines sky high HP with good special, moderate attack and defense ratings, with below average speed. Lapras is basically a cooler looking Starmie with no Recover. You can slap Rest on him, I personally don't, but I have seen it. There isn't really much to explain how he works. He's got good durability and versatility. Use him well.
