Ice-types are my 4th favorite Type of Pokémon.

Unlike Dragons, Ghosts, and Water-types, Ice-types have many weaknesses, and don't work well on nearly as many Types as those ones, either.

The strengths of the Ice-type are more unique, such as their ability to Freeze opponents, or their ability to take advantage of Hail.

1. The Snowstorm Strategy

Ever since Gen 4, the best strategy for most Ice-types has been the Blizzard+Hail combo.

In Hail Weather, Blizzard ALWAYS hits, and because Blizzard is quite powerful, hits multiple opponents, and can even Freeze them sometimes, this is an EXTREMELY effective strategy.

Add to this Abilities like Snow Cloak (which can be combined with Evasion increasing Moves and Held Items) and Ice Body (which can be combined with Leftovers, and even Aqua Ring), as well as the Gen 7 Move Aurora Veil (A 2 in 1 Light Screen+Reflect Move, that only works in Hail), and you have a VERY powerful Weather based strategy.

Also keep in mind that the Ability Snow Warning is ALWAYS the best way to make it Hail, as it doesn't take a turn to use it.

In fact, sending out a fast Ice-type (like Froslass) that knows Aurora Veil, and that is holding a Light Clay, paired with a Pokémon with Snow Warning (such as a Hidden Ability Aurorus, or an Abomasnow), is quite possibly one of the best Ice-type strategies there is.
(In a Single Battle, a Hidden Ability Alolan Ninetales could do the same thing, as it is fast AND has Snow Warning.)

One advantage the "Snowstorm Strategy" has over other Weather based strategies, is it's less Weather dependent than most of them.
(Blizzard works fine in other Weather Conditions, and Aurora Veil doesn't disappear when it stops Hailing.)

2. Offensive Weaknesses

Ice-type Moves have trouble against Fire, Water, Ice, and Steel-type opponents, and it can be hard to cover all of those different weaknesses sometimes.

If learnable, Freeze-Dry is your best way of dealing with Water-types (just read my Water-type Blog, lol), and for Fire-types, Water Moves work well.
(Most Ice-types can at least learn Water Pulse, although it isn't very powerful.)

For Steel-types, Shadow Ball works good, as do Water-type Moves, but it's best if you have a secondary Type that either does OK against Steel-types (Water, Ghost, Dark, etc.), or good against them (like the Ice/Ground-type Mamoswine).

Many of the more Physical Ice-types can learn moves like Brick Break, or Earthquake, so these should be considered, as well.

3. Defensive Weaknesses

As always, if doing a Team focused on a single Type, it's best to have a variety of secondary Types, both for a variety of different Attacks, as well as to cover your common weaknesses.

In the case of Ice-types, you have to worry about Fire, Rock, Fighting, and Steel-type Moves.

There are many cool Ice/Water-types out there, and they fair well against both Fire and Steel-type Moves, as well as being able to use powerful Water-type Moves, which work well against both of those Types, as well.

For Fighting-types, there's always Froslass (one of my favorites), which is an Ice/Ghost-type, making it completely Immune to Fighting-type Moves.
Other good options include Articuno, Jynx, or an Alolan Ninetales, all of which are not only resistant to Fighting, but also have powerful Moves that do good against Fighting-types, as well.
(Froslass CAN learn both Psychic and Fairy-type Moves, as well.)

4. Freezing

Other than doing VERY well against Dragons, the biggest advantage of Ice-type Moves is their ability to Freeze.

Unfortunately, there's only a 10% chance of this happening, and very few ways to increase those odds.

The Ability Serene Grace increases the chances of Ice-type Moves Freezing, but as of Gen 7, there are no Ice-types that actually get this Ability.

If in a Double or Triple Battle, or a Battle Royal, using Blizzard increases the odds of SOMEONE getting Frozen, simply because it hits multiple opponents.

However, it's best not to try to Freeze your opponents, as it's too unreliable as a strategy.

Instead, Freezing should be looked at as a nice thing that happens occasionally when using your Ice-type Moves.

BTW, the highest possible chance of Freezing an opponent is 60%.

This would be if a Pokémon with Serene Grace (like Blissey or Togekiss) uses the Move Secret Power in a Battle taking place on Icy/Snowy Terrain.
(If they ever add a Move/Ability that causes those Terrain Conditions in Battle, this may be EXTREMELY useful to know.)

5. Mega Evolution

There are only 2 Ice-type Mega Evolutions, the fewest of any Type.

They are Abomasnow and Glalie, and they both have their advantages.

If you want to use the "Snowstorm Strategy", and have no other Pokémon with Snow Warning, then Abomasnow is the probably the way to go.

If you like Refrigerate (which is EXTREMELY powerful when combined with moves such as Hyper Beam, or Explosion), then Glalie is best.