Comments with a number of point values.

Faction Power - Blood of Ice - Dwarfs of the Frozen Plains gain a +2 on all fear based courage checks.
Spend a command action to mark "Song of Elhaz" - You may spend a Command Action to empower one of your units with Elhaz, Song of the Guardian, that unit gets a permanent defensive +1/+1 vs ranged attacks. the mark is erased and the bonus lost if the unit routs.
The Blood of Ice is a nice cookie for units that live with big monsters and aren't easily scared.
Song of Elhaz I don't like for a few reasons. A lot of times it will be dead. Other times the opponent will be able to cancel it with a command action of their own (target a different unit). It will only be really good when someone has multiple ranged units attacking a single guy, which shouldn't ever happen given that you can use the Song so brutally against any such attempt.
If you want to make your guys harder to hit, I'd suggest using command cards that are normal-power vs. non-ranged attacks and buffed vs. ranged attacks.
Dwarven Axemen (core)
Offense: (5)5/5 Defense: 2/3 Range: - Courage: 12 Move: 2.5" Hits: 4-4-4
MC 3.5" when Routing or Final Rushing.
233 points. This may be slightly too high, as I've charged the Dwarves for the same MC as Runegard. They get the 3.5" for final rushing and routing, but without the generic sprint ability it could be argued that they should be a bit cheaper. As a point of reference, they would be 214 points if they only moved S.
Shaman Drummer (core)
Offense: (3)4/4 Defense: 1/3 Range: - Courage: 12 Move: 2.5" Hits: 3-3-3
MC 3.5" when Routing or Final Rushing. Cannot drum while engaged. Drum Range: 6".
Songs: Othalla, Manaz
80 points for the unit itself, but obviously what has to be figured out is how much its spells are worth.
Dwarven Bowmen (core)
Offense: (4)5*/5* Defense: 1/2 Range: 14" Courage: 12 Move: 2.5" Hits: 3-3-3
(-0) -2/-2 and while Engaged. MC 3.5" when Routing of Final Rushing.
171 points.
Dwarven Spearmen (core)
Offense: (6*)5*/5* Defense: 2/3 Range: - Courage: 13 Move: 2.5" Hits: 4-4-3
(-1) -0/-0 while Charging. ?(+0) +1/+0 vs. Cavalry and/or Large units. ?(+0) +0/+2 while Holding vs. Charging Cavalry and/or Charging Large units. MC 3.5" when Routing of Final Rushing.
272 points, but I'm a bit puzzled by some of the specs. Why do these guys have one less hit (11 total) than Axemen and why one more courage? One of the things we normally do with Battleground is to establish a baseline for a faction's infantry and then every deviation from that baseline is explained in terms of something specific, e.g. equipment, training. Dwarven Axemen should normally be the baseline unit, so having fewer hits would suggest a less dense unit which doesn't seem to apply here. The point of courage isn't a problem, but it's not clear to me why it's there.
Reindeer Cart (core)
Offense: (4)5*/5* Defense: 2/2 Range: 14" Courage: 12 Move: 5" Hits: 3-2-3
Cavalry. Wheeled. +2 Impact Hits. (-0) -2/-2 and while Engaged. You may use any side of this unit as the front when making ranged attacks.
An entertaining take on the High Elf chariots, in particular the folks who said, "Hey, chariots were mobile platforms for archers." My problem is mainly that +2 impact hits is kind of silly if your base stats are falling to 3/3.
Dwarven Battleaxemen
Offense: (5)5/6 Defense: 2/3 Range: - Courage: 12 Move: 2.5" Hits: 5-4-3
MC 3.5" when Routing or Final Rushing.
286 points. Another example where equipment should set the stats -- the Battleaxe gives +1 power on offense, but you've chosen not to give them -1 defensive skill (no shield). Why? Also, you've given this unit an extra green hit (in exchange for a red) which suggests they maintain unit cohesion better when taking casualties but they aren't one of the units you've chosen to give above-average courage to.
Dwarven Frostbeards
Offense: (5)5/6 Defense: 2/3 Range: - Courage: 14 Move: 2.5" Hits: 4-4-4
MC 3.5" when Routing or Final Rushing.
309 points. These guys don't feel distinct enough.
Dwarven Walking Armoured
Offense: (4)6/6 Defense: 3/3 Range: - Courage: 13 Move: 2.5" Hits: 4-4-3
Defense +1/+1 vs. ranged attacks.
370 points -- estimated, since new abilities are always tricky to cost. Why are they short a hit compared with other units?
Polar Bear Riders
Offense: (6)5/6 Defense: 2/2 Range: - Courage: 12 Move: 5" Hits: 4-3-3
Cavalry. +1 Impact Hits.
I wasn't sure if this unit was supposed to get the normal cavalry charge bonuses (plus an impact hit) or not. Can you clarify?
Wild Mammoth (Elite)
Mammoth: Offense: (5)6/7 Defense: 1/4 Range: - Courage: 11 Move: 5" Hits: 7-5-5
Colossal. Terrifying. Always has the "Close" Standing Order and may not be given a Standing Order Modifier or be directly controlled. To play Command Cards on Wild Mammoth you must first discard two other Command Cards. Wild Mammoth requires two Command Actions to Rally. Cannot be the target of Drummer Songs or empowered with Song of Elhaz. (+0) +0/+1, +1/+0, and +2 Impact hits while Charging. (These are in addition to the normal Charging bonus.)
484 points. He's a big boy, isn't he?

Trained Mammoth (Elite)
Mammoth: Offense: (4)6/7 Defense: 2/4 Range: - Courage: 13 Move: 5" Hits: 6-5-6
Side Archers: Offense: (3)5/5 Range: 10.5"
Colossal. Terrifying. Cannot be the target of Drummer Songs or empowered with Song of Elhaz. Trained Mammoth has three sets of attacks that are rolled independently; the mammoth itself (main stat line) and archers mounted on the sides (stat line on side). Attacks can be made againest different targets.
Mammoth Attacks: (+0) +0/+1, +1/+0, and +2 Impact hits while Charging. (These are in addition to the normal Charging bonus.)
Side Archer Attacks: This is a ranged attack even when Engaged. (Does not recieve Engaged combat modifiers and gets no Free Attacks vs. Routing Units and no attacks on opponents turn.) The archers consider their front arc to be the side of the mammoth they are on. No penalty for Move and Shoot.
Over 700 points, including over a hundred for the missile fire.

Drummer Spells:
Song of Othalla - Give an unit within Drum Range Defense (+1/+1) until your next command phase
Song of Mannaz - Give an unit within Drum Range Courage +2 until your next command phase
Song of Thurisaz - Give an unit with Drum Range the Fearsome trait until your next command phase
My first thought is that I was disappointed that the drum spells worked just like other spells. Since they are based on sound, I was hoping for area affects, even though I recognize that such things are much harder to cost properly. That aside, I have a few concerns. First, Othalla is going to trump the other two most of the time. Mannaz will occasionally be great, but it suffers from timing -- you only cast spells on your turn which means you'll always have to use it on a unit that might take a rout check, never on one you know is going to. In many of those situations you're still going to be better off giving a unit D+1/+1 than +2 Courage, since that kind of buff might prevent the check or might keep it from being a check in the red (or prevent the unit from being killed instead of checking in the red).
You also need to clarify how these spells work wrt command cards and with each other. I would suggest at least the following modifications:
1. All songs create blessing tokens. This prevents stacking and also makes them a bit worse in general.
2. Mannaz lasts until after the next courage check. This makes it much better, of course!
3. A unit blessed by Othalla cannot benefit from defensive command cards.
4. Thurisaz lasts until the unit routs. (Naturally it will also end if the unit gets a different bless.)
3x Song of Isa - The Song of Ice lowers the maximum move of an enemy unit to 2.5" for one phase, play before opponents Movement and Command phase.
3x Song of Uruz - The Song of the Fearless Beast grants one of your units a MC of 5" when Final Rushing.
3x Song of Ingwaz - The Song of the Hero grants one of your engaged units a free attack during the Post-Combat Courage Phase even if the opposing unit is not
routing. Give the attacking unit one damage.
Isa is too weak to be a command card, let alone one that is a 3-of. (We don't normally do 3-ofs anyway.) Sometimes it will be amazing, but usually it will be weak.
Uruz -- good, but MC cards usually need some extra cookie or alternate use. Compare with Aspect of Wolf.
Ingwaz -- Interesting! May be way too good, but I'm intrigued.