What is Freeze in Hearthstone?
Hearthstone has many card effects that are common enough that they get their own keyword - a word or two that immediately tells you how the card works. Let's take a look at the Freeze keyword.
Frozen characters lose their next attack.
The Freeze keyword does exactly what it sounds like it does. It freezes stuff. Freeze as an effect however works slightly differently than some people believe. If a character is Frozen, it simply misses its next attack. If a character that could attack this turn is Frozen before attacking, it will lose the attack and it will thaw at the end of the turn. If a character that already attacked this turn (or couldn't attack due to summoning sickness) is Frozen, it will stay Frozen until the end of your next turn since the next attack for it to miss is your next turn. This is quite important for cards like Cryostasis. Note that having 0 Attack or "Can't Attack" does not affect the Freeze duration.
Freeze effects are mostly relegated to Mage, but they do occasionally appear in Shaman as well. There are also a few Neutral cards with the effect.
Keywords that Work Great with Freeze
Keywords that work great with Freeze are difficult to define properly as Freeze is a status condition applied to enemies by the player and there are no other mechanics like this in the game. Theoretically, if you're playing a Freeze-centric deck, you're probably playing a stall/Control deck, and therefore defensive-oriented keywords like Taunt would make sense there.
Playing Against Freeze in Hearthstone
If you're opponent locks your board down with a Frost Nova or Blizzard, it's unlikely that all 7 of your minion slots will be taken up, so you can still play other minions. In any case though, removal and AoE spells can help clear your opponent's board away which is useful if a Freeze AoE is paired with Doomsayer. Silencing a Frozen minion will thaw it, although this will require you to run a Silence card in your deck, many of which are situational.
Against a card like Water Elemental which will Freeze what it damages, consider what minions you run into it to kill it. Using spells can get around that problem altogether.
Example Freeze Cards in Hearthstone
Water Elemental is a Mage card in the Basic set, meaning every player has access to two copies of it. It's a strong 4-drop with good stats and a strong ability, not to mention also an Elemental. It doesn't see as much play as it used to, but it's still a good card to consider for many Mage decks.
Frost Nova is... another Mage card in the Basic set. A strong one too, locking down your opponent's current board for a turn, saving you some damage and buying you some time. Especially strong when paired with Doomsayer.
Snap Freeze is a card that specifically interacts with Frozen minions, which is fairly rare. You can Freeze a single target minion, but you can also target a minion that's already Frozen and destroy it. Strictly better than Shatter for all practical gameplay purposes.
Moorabi is an infamous card, part of the infamously undersupported and underpowered archetype of all-time: Freeze Shaman. It's often viewed as one of the worst Legendaries in the entire game, so I would recommend not playing it unless you're playing it as a joke. If you are playing it as a joke though, don't expect to win very many games with it.