As Glacial Prison applies Frost to enemies hit in a large area, you can initiate fights by combining it with Arctic Assault and Permafrost. After your stun, enemies will still be nearly immobile, giving your team a few seconds of time in which to crush key targets.
Remember that Glacial Prison explodes at the end of its range if it does not collide with an enemy champion. This actually gives it additional range and capabilities if you wish to make use of of it. Sometimes you can purposely avoid hitting a specific champion to hit more targets overall. Although this wil result with only slowing champions and not stunning them.
Your Permafrost has a rather impressive 1000 range. Consider waiting for your opponent to use an escape ability before using it (As long as Frost is applied for up to 3 seconds, it can be used from afar). This allows you to close a gap when they least expect it. Your Glacial Prison can also be used to close the gap, due to it's similar ranged capabilities.
Frozen Mallet is typically the better choice, with a higher slow and bonus health, however Rylai's Crystal Scepter may be taken if you expect the need of another AoE slow source and higher ability power.
Buying a Sunfire Cape allows for continuous damage on enemies, used in combination with slows it can rack up a lot of damage over a period of time. It also improves her Flail of the Northern Winds ability due its health scaling, adding up to 81 total bonus damage on a single cast to enemies suffering from Permafrost.
Much like Leona, building Sejuani as a full AP caster is not ideal due to her low AP ratios.
Randuin's Omen provides another extremely powerful active, as well as many of the stats Sejuani needs, and an anti-dps passive on-being-hit.
Frozen Heart may be the most important item for Sejuani, as it provides a very large amount of armor and, more importantly, CDR, which helps deal with her very long cooldowns, on top of an extremely powerful defensive aura.
Guardian Angel is also a reasonable item for Sejuani late game given that her role in team fights is generally to charge straight into the enemy and hamper them with her AoE skills.
Ultimately, CDR is Sejuani's most important statistic to itemize or build for. Building an early Glacial Shroud and Kindlegem after GP10 items is arguably Sejuani's best early build. Also consider playing with a team that can allow you to take the second and/or third blue golem. This is ideal for before you gain the CDR required to combo your abilities efficiently.
Consider getting a Spirit Visage after getting Warmog's Armor, as not only it gives you a massive 20% CDR, but increases your HP regen, and gives you a big MR boost.
Because of her early game weakness, buying wards is crucial to protect both you and your jungle. Although rushing a Sightstone is not recommended, as it will delay your build, try and grab one early game to protect your jungle entrances.
If you are extremely fed, proceed to upgrade the item to Ruby Sightstone as it will give you 1 extra ward and increase your W dps.
You can also ask your top and bot to ward those jungle entrances, leaving you to cover the near mid lane entrances.
Iceborn Gauntlet synergizes well with Flail of the Northern Winds, as upon activating it you can land a double enhanced autoattack, that will deal twice as much damage and also slow any nearby enemies, keeping them in range.
The first point in Flail of the Northern Winds is necessary to get your jungle started, as it has the highest Area of Effect damage on level 1.
To clear a jungle camp, DO NOT start with Arctic Assault. Instead activate Flail of the Northern Winds to apply Frost to all the monster in the camp. Shortly before Frost is about to expire, refresh its duration with Permafrost to do a sizable amount of damage. Save Arctic Assault for leaving the camp, or escaping a possible gank.
Sejuani is an extremely potent ganker once she hits level 4. Refrain from boldly pushing your lane if you believe she's reached this level. Even before level 4, her ganks can still hurt, so always have a ward in place to prevent getting jumped.
Once she has a few levels going for her Sejuani is a very proficient farmer, so it would be wise to try and stop her from farming too much throughout the game, or she may become extremely difficult to deal with/kill later on.
Glacial Prison is a very powerful initiation ability, and if multiple teammates are caught in it, it could prove a difficult recovery. Avoid bunching up while she is near and/or making yourself an easy target.
Once Sejuani catches you alone, escape is nearly impossible. Avoid invading her jungle if she's made herself difficult to kill and you are unsure of her position. Also, avoid pushing lanes by yourself if you are not certain you can kill her or get away, or of her location.
Sejuani is extremely weak at dueling other champions in the early game, but will become extremely strong if she doesn't fall behind. Due to being one of the most powerful champions in the lategame, it's important if your team can focus on shutting her down. Try counter jungling and playing safe so she can't gank lanes successfully. Coordinate strategies to keep her behind without farm. Take advantage of her glaring early game weaknesses.