Hearthpwn

I've been creating my own freeze mage decks from scratch, and when I browse others you obviously see a lot of similarities.  One thing, though - why does almost every freeze mage run two Arcane Intellect?

We generally dont run Mana Wyrms or Gadgetzan Auctioneers in our freeze decks, and the only freeze deck that tends to run Sorc Apprentice is the OTK style deck (which I dont personally care much for).  There's nothing to combo Arcane Intellect for synergy.  You're taking up space in your deck with cards that cost 3 mana to cycle cards.  I prefer to run additional card draw minions in place of arc. int., like loot hoarder, novice engineer, acolyte of pain, etc. for board presence.  (I mean additional as in adding in the one of those 3 that you dont already have.)

Finally, I occasionally, but rarely run Coldlight Oracle because I dont like to help certain opponents like rogue and hunter - which can be a favorable matchup for a freeze mage in many cases.

I would say Ysera or Raganos Firelord. I think Raganos would be nice to draw removals plus you get an immediate return when u play him

Please explain mulligan phase.

I 

Mulligan refers to when you're shown your first hand and keep or replace cards. "Mulligan for X" means discard everything that's not X in hopes of getting X. 

I think its important to play your secrets early in the game, so I always keep at least one or two secrets.  you want to keep your health up as much as possible early in the game, so play the Ice barrier first, then the block.  It's important to get the block played, because you will usually need it.  I sometimes will keep the Alextrasia at the beginning as well as it's essential in most games.  I also keep the doomsayer, and usually play it on tuen 2 or 3, which in many cases will get rid of your opponents initial minions, and prevent them from playing a minion on turn 3, and instead focus on either destroying your doomsayers, thus using up a lot of their cheap damage spells, or preventing them from playing a minion on turn 3.  If they have the coin, then they can usually destroy your doomsayers on turn 3.  

Avoid using your ice lance and frost nova until late game if you can.  I prefer to take small amounts of damage early in the game, protect myself with doomsayer, ice barrier.  I try to save my mirror image for late game if possible.  Depending on the class of your opponent, you may have to use it early. 

many games Ill let them get me down to low HP as long as I have the ice block up, and one in my hand, especially if I know I have the freeze spells to prevent them from attacking over the next few turns while I play out my Alex, and finish them off

so to sum it up, I keep the secrets, doomsayers, and the novice engineer or Alex/Archmage.

I've really enjoyed this variation, after spending a while trying to get better with otter's deck I often found that I wish I couldve included a little more burn in it. Having pyro + antonidas gives it just what it needs. 

However I don't agree with Maly. I often find he's way too big of a target and will often not survive even a single round late game if he's the only thing on your board. Along with that, the time that you can finally drop him is one of the most important last phases of the game where every turn is important. 

malygos is a bit overkill id say.

It really helps out if you had to use Alexstraza to bring yourself to 15 health in emergency situations.  I first used mountain giants, but found that Malygos was much more beneficial.   As no deck is perfect, having this card gives you some insurance as well as another avenue for the end game, especially if you had to use some of your damage spells to kill the other players minions, and didn't have enough damage output left to finish him off.

I think so, unless you have a way to ensure Malygos stays alive to the next turn. A possible combo is Malygos+arcane missiles, but what are the odds that you haven't used AM at least once since the beginning of the game? Not my favorite legendary for mage. Now, for warlock, with double soulfire, he really rocks even if he's removed ;)