DO NOT allow this homebrew. In fact, until you're vastly more experienced both at DMing and at 3.5 optimization, do not allow any homebrew whatsoever. Restrict your players to a few books (Core only, plus Completes if you feel you can handle it), and slowly build your game skills from there.
The three abilities you've posted alone are quite, quite unbalanced. This guy seems to know what he's doing, since the thing he seems to aim most for is breaking the action economy. Whenever I read 'swift action' in an ability's description, I get leery. When I read 'free action' or even 'nonaction', I'm not inclined to believe my eyes, unless the ability granted is really weak.
The ones you posted are NOT weak. In fact, the Sleet Storm effect is likely to totally dominate any given combat, while the Wings of Cover thing (as a nonaction...

) makes him effectively invincible. Instant Death is just icing

.
The ability to control lots and lots of undead underlings is obviously a method of breaking the action economy even further. The rest of the class seems along the same lines.
The 'weaknesses' built into it (low HD, middling BAB, relative lack of powerful spellcasting) are just methods to divert attention from the class' broken abilities.
Let's take a step-by-step:
Tomb-Tainted Soul, gained at 1st level, is better than the feat of the same name. Even Dread Necromancers must take the feat and don't gain it as a bonus feat.
Control Ice, gained at 1st level, is an at-will move action that can be used to force enemy creatures to move away. The author goes to great lengths to explain how this is not able to trap enemy creatures - thus diverting attention from the fact that he'll be able to
do it all the time without spending his standard action, rearranging the battlefield (probably even creating difficult terrain etc.) as suits him.
Rime Dragon (2nd) is basically Eldritch Blast plus Repelling Blast, that gets bigger with levels. Warlocks would like to have this.
Frost Blade (3rd) is a multipurpose tool that grants very high Cold Resistance for the level and can be used to deal damage, debuff opponents, and do Spiked Chain goodness. It also seems this Spiked Chain is an extra attack that happens
without taking up an action.
Inspirational Fighting (4th) is about a +2 bonus to attack and initiative at low levels, much more at higher levels.
Effectively makes up for the middling BAB.
Animate Dead (5th) is a spell-like ability for this guy, so he saves
a lot of money on that black onyx.
Flash Step (5th) is a
per encounter,
swift action teleportation effect. At 5th level. Ouch.
Undead Commander (6th): You gain Leadership (which may be the only broken feat in Core),
but much better, as a bonus feat. Nuff said.
Boreal Winds (7th): A 5th level spell as a spell-like ability several times per day. At 7th level. Nuff said, once again.
Bonus Feats: He gains 5 Corpse Crafter or Leadership bonus feats. I'm beginning to wonder what he'll use his regular feat slots on, since all the stuff that would be good with this class' abilities he gets as a bonus feat...
Boreal Haze (8th) will begin this guy's total dominance. Up to now, he's been better than others, but not outright broken. From now on, expect every battle to go exactly as this guy wants it: on his turn, he'll activate it (
swift action), and whenever he feels an ally might be able to do something effective, he'll turn it off (free action). He'll not only be able to see in the Boreal Haze, but also detect invisible creatures (something he couldn't do until now), eliminating a potential weakness of this class. Use whenever you feel like it, for just as long as you need it! His Cohort is, BTW, unaffected... horrible stuff, to be sure.
Undead Legion (9th) finally puts Dread Necromancers in their place where controlling undead is concerned. Was about time.
Dragon Form (10th): very good self buff, usable as a
move action, and
1/encounter. Arguably as good as or better than Barbarian Rage. I'm detecting a theme here.
Arctic Pillar (11th): I'm not really getting this ability, it seems a no-save instant kill to anything up to a CR of this guy's level. The "This ability affects the Uttercold Marshal" clause is actually good for the Marshal, as it heals him instead of damaging him. We're slowly advancing into total brokenness wonderland here.
Guardian Wings (12): Flight, sure, why not, you need it at this level, even if the maneuverability is perfect. Another potential weakness covered. Plus Wings of Cover (good, even broken spell on its own) without even spending the immediate action on top of that? Wow. I'm not sure what to say. This guy is now
immune. As in, to whatever happens to come up.
Greater Rebuke (14th): Aside from the fact that at 13th we only gain a bonus feat (what's happened to our beautiful 'one-overpowered-class-feature-per-level' rule?!), this puts things right again, in breaking the undead control even further. Do you have any idea what epic-level monsters this guy can have hanging around now?
Grave Knight (15th): 'Look mommy, I just gained 16 points of ability score bonuses!' Plus other good stuff, of course. This isn't even the capstone. I'm feeling we're far beyond the borders of Ridiculoustan by now.
Demonic Ice Mirror (17th): Now this is approximately the equivalent of a 9th level spell, which is OK for the level. The Marshal can use it 1/encounter without spending resources, though.
Great Leader (18th) won't do much, it's only followers after all...
Legendary Commander (20th): As a capstone, we gain an epic feat (just) before epic levels. Hmm.
(I'll not go into spells - they're good, but seem more of an afterthought.)
Most of the stuff here aims at three things:
1. breaking the action economy (getting effects for no or little actions yourself; denying actions to your enemies; followers and cohort, animated Undead, and controlled Undead make for many, many effective bonus actions),
2. getting benefits without opportunity cost (lots of bonus feats; lots of per-encounter powers; underlings provide additional versatility),
3. saving on the character's resources (effects like flight and detection of invisible creatures, which don't seem like a natural forte of the class' theme and would consequently have to be bought as items, are granted as class abilities for no reason at all; spell-like abilities use no costly materials, especially black onyx).
Seriously, the very fact that you have to ask about his homebrew's viability shows that you need to get more experience under your belt before you even think about allowing homebrews!