Eh, I think it might be easier if you look at things from a Nerf/Buff comparison.
Frost Armor - INNATE: Sejuani gains 10 / 15 / 20 / 25 bonus armor and 10 / 15 / 20 / 25% Slow Resist for 2 seconds upon damaging an enemy with an ability or a basic attack (stacks up to 3 times for a 6 seconds maximum duration, afterwards refreshing with further damage applications)
Frost Armor - After not taking damage for 15 seconds Sejuani becomes immune to slows and gains [100% total Armor + flat 100] Armor and [100% total MR + flat 100] Magic Resist. Frost Armor persists for 1/2/3 second(s) [at levels 1/7/14] after taking damage. Frost Armor refreshes faster as Sejuani moves.
Old version is geared towards durability in prolonged encounters. New version is stronger against initial burst but vanishes entirely in prolonged fights. This passive change is also a hit to early game jungling, because you get more durability taking camps (up to 6 seconds) compared to that one second of high durability the new passive grants.
Arctic Assault [Q]:
RANGE: 650
80 / 85 / 90 / 95 / 100 mana
15 / 14 / 13 / 12 / 11 sec Cooldown
Sejuani signals Bristle to dash forward, dealing 80 / 125 / 170 / 215 / 260 (+ 40% AP) magic damage and Airborne icon knocking up all enemies he passes through until the charge ends or upon colliding with an enemy champion.
Arctic Assault [Q]:
70/75/80/85/90 mana
13/12.5/12/11.5/11 sec Cooldown
Sejuani charges, dealing 60/90/120/150/180 (+40% AP) magic damage to enemies and knocking them up for 0.5 seconds. The charge ends after hitting an enemy champion.
There's some slight reductions on the mana and cooldowns in exchange for damage. I'd label this as an overall nerf.
Flail of the Northern Winds [W] :
RANGE: 350
40 / 35 / 30 / 25 / 20 mana
11 / 10 / 9 / 8 / 7 sec Cooldown
Sejuani's next basic attack deals bonus magic damage (4 / 4.5 / 5 / 5.5 / 6% (+ 3% per 100 AP) of target's maximum health) to all enemies around the main target (capped at 300 against minions and monsters)
After landing the enhanced attack or upon reactivation, Sejuani rotates her flail about herself for the next 4 seconds, dealing magic damage [TOTAL MAGIC DAMAGE: 40 / 70 / 100 / 130 / 160 (+ 4 / 6 / 8 / 10 / 12% maximum health) (+ 60% AP)].
Winter's Wrath [W]:
60 mana
7/6.5/6/5.5/5 sec Cooldown
Sejuani swings her flail, dealing 12/19/26/33/40 (+1% total health) physical damage and applying Frost to enemies hit.
She then lashes out with her flail, dealing 48/76/104/132/160 (+4% total health) physical damage and applying Frost.
Winter's Wrath deals 20% bonus damage to monsters.
Old version allowed for an AP Bruiser build, which would easily outperform the new iteration in terms of damage. A Rod of Ages+Liandry build would hit ridiculously hard. Comparing straight health builds, I still think we are seeing a weaker W because of the scaling maximum health numbers as compared to the fixed max health numbers in the new iteration. There won't be a notable difference in the early game (before items), but it's kind of sad to see a late game nerf here with no real early game compensation. Mana costs are up considerably as well. I can only hope that PBE is missing a scaling maximum health component.
Permafrost [E] :
RANGE: 1000
55 mana
10 / 9 / 8 / 7 / 6 sec Cooldown
PASSIVE: Sejuani's basic attacks, Arctic Assault, Flail of the Northern Winds, and Glacial Prison apply Frost to enemies hit for 4 seconds.
ACTIVE: Sejuani consumes Frost on all nearby enemies, dealing magic damage (80 / 105 / 130 / 155 / 180 (+ 50% AP)) and slowing them (50 / 55 / 60 / 65 / 70%) for 1.5 seconds.
Frost cannot be reapplied on the same targets until 3 seconds after Permafrost's duration ends.
Permafrost [E]:
20 mana
1.5 sec Cooldown
Passive: Nearby melee allied champions' basic attacks apply Frost to enemy champions and large monsters.
Icebreaker: Enemies stunned by Sejuani are frozen, causing Sejuani's first attack or spell against them to deal 15/20/25% of their maximum Health as magic damage (max 400 vs monsters). [Moved this here because it felt appropriate]
Active: Target enemy with 4 stacks of Frost takes 40/60/80/100/120 (+30% AP) magic damage and is stunned for 1/1.25/1.5/1.75/2 second(s).
An enemy that has been stunned by Sejuani cannot gain Frost stacks for [9???] seconds
Honestly the old version of E was fairly strong for it's reliability. With 40% cooldown and a button press for AoE CC, it was possible to keep every enemy in an almost permanent slow status late game. While the new version allows melee allies to apply frost stacks, you have to recognize that there was no stacking mechanism in the old E. You only needed one stack of Frost to trigger Permafrost. The active damage on the two skills are not even comparable, since one could hit AoE. You literally need the Icebreaker passive to be considered for the new Permafrost to even come close to making a decent single target damage comparison. PBE is still unclear if there will be a reduction in time for how quickly immunity from Frost stacks fall off (I know it is 9 seconds at Rank 1 E simply because of the image). The skill will certainly "feel" more rewarding to execute properly, but I don't think the actual numbers will reflect that effort. The Icebreaker nuke at 15% for Level 6 champions is going to be around 150 damage on anyone running around with 1000 health which can eventually become ridiculously strong late game when you're blasting squishy targets for a quarter of their health bar regardless of how much current health they have. There's such a dramatic shift in how her damage here is best utilized that it is difficult to classify it as a buff or a nerf. It's like we buffed late game dueling capabilities but nerfed late game teamfighting capabilities... on a tank.
In a comparison of using W+E together for jungle clearing at early levels, the new iteration is stronger on the condition that you hit most of your W damage. But she is not nearly as durable in the early game. So... higher potential damage but squishier.
Glacial Prison [R]
RANGE: 1175 / 225
SPEED: 1350
100 mana
130 / 115 / 100 sec Cooldown
Sejuani throws a frost-forged bola in a line, shattering upon colliding with an enemy champion or upon reaching maximum range, dealing (150 / 250 / 350 (+ 80% AP)) magic damage to all enemies in the end area. Enemies in the end area are either stunned for a short duration if the bola hits an enemy champion or slowed by 30% for the same duration if it reaches maximum range.
Glacial Prison [R]:
100 mana
120/100/80 sec Cooldown
Sejuani throws her True Ice bola that deals 75/125/175 (+40% AP) magic damage to the first enemy champion hit and stuns them for 1 second.
The bola becomes more powerful as it travels, doubling the damage and stun duration and creating a storm that slows other enemies by 30%. After 2 seconds, the storm deals 150/250/350 (+80% AP) magic damage and slows by 80% for 3 seconds.
Short range Ult has been nerfed, but the long range Ult appears to be the same. The short range Ult will do more damage if you can manage to keep your targets in that zone for the Storm damage to apply. I'm thinking this might actually be a buff? It looks like it should be, unless I'm missing something (like no damage or storm zone if you miss your ult).
Overall... I think Sejuani is going to be more difficult to play. She's lost a lot of reliable damage and utility. I tend to dislike when champions become harder to play with no substantial reward for that transition.