You can play any way you want to and do not have to jungle. However, some champs are so good at jungling, that one usually prefers that to normal laning (Amumu, Shaco, Skarner and the like).
You are right, that a jungler means that one other player is left alone against two enemies. However, he has the protection of a turret, which is enough in the early game to survive. Plus, he levels almost twice as fast as his two enemies, so he will very soon have his ultimate available against two level 3 or 4 enemies. Of course, some champions have a hard time to stay alone in a side-lane. Make sure when you have a jungler in your team, that you have a solo-champ that can hold its own without problems.
Jungling can only theoretically be done by all champions (sure, anyone can go into the jungle and attack creeps there). However, most champions are way too slow to make it worthwhile. They would profit much more from staying in a lane. These champions should not try jungling. If you want to try jungling yourself, then select a champion, for which you have one of these jungling guides at hand. Don't just try any random champion out in the jungle.
Finally, the most important point about jungling is one that most novice players often forget. You do not jungle in order to remain in peace and level up on your own. You jungle, so you can level up and at the right moment appear in a lane for a surprise gank. Enemies have to be constantly aware that a jungler may pop out of a nearby brush all of a sudden turning their 1v1 or 2v2 lane into a 2v1 or 3v2 problem. If done right, jungling can very quickly devastate your enemies, because the jungler has the power to turn around any lane. If one of your team's lanes is having trouble, adding another champion to it will devastate the enemies and at least break their attacks. Often, you can even net a kill or two. If you're a good jungler and help out frequently with ganks, then you will soon outlevel your enemies and the game can be pretty much decided in less than 20min.
So in summary, do not doubt jungling. It is a very popular and strong strategy. However, be aware that being a good jungler is not easy. Especially, when playing together with other novices, who may not know how to deal with a jungler in their own team. I suggest, you try to get at least several dozen games of normal lane-gameplay done, before you try out jungling yourself. And then, start with practice games, so you are certain, that you will survive the early jungle farming. It is most embarassing to die to the golem when no enemy was ever present.
Best Answer
I am a fan of Sejuani jungle but it can indeed be very difficult! With the setup I use I tend to do fine, so I'll just list that for you and you can tell me whether it was helpful to you or not!
I use: Attack Speed Reds Armor Yellows Magic Resist/lvl Blues Movement Speed Quints
The attack speed on Sejuani helps when clearing camps and also allows you to attack faster during your ganks with your permaslow skill set + red buff. The armor amount on yellows is higher than on blues or reds, and hp/lvl does not really help Sejuani's early game, which is where she needs the most in my opinion. I use Magic Resist/lvl blues in order to have the ability to not get melted by mages if I find myself building armor against the enemy team, or to get ahead in magic resist if against a heavy mage team. Movement speed quintessences on junglers, especially Sejuani are very helpful giving you more speed inbetween camps and when ganking lanes.
I use 0/21/9 Masteries, the same as you do. I get the movement masteries in both the defensive and utility trees. I also get the minion damage return from the defensive tree as well as the 2 point damage reduction.
I start with Regrowth Pendant and a Health Potion. I go Wolves -> Blue -> Wraiths -> Golems -> Wolves and recall and buy Philosopher Stone. When returning to your jungle, clearing your red buff will get you to level four and you will be ready to gank with your perma-slow skill set and red buff slow.
At this point, you want to find a nice balance between ganking and jungle clearing. The faster you get to level six, the more deadly your ganks will be. If no lanes are struggling, I would suggest that you try to rush that level six so that you can unleash icy wrath on your opponents!
My full item build on Sejuani looks something like this:
Ninja Tabi/Merc Treads Randuin's Omen Shurelya's Reverie Frozen Heart/Sunfire Cape Banshee's Veil/Force of Nature Abyssal Sceptre/Deathcap
I like Sunfire on Sejuani because it synergizes well with her W skill and the damage really does add up. And as Sejuani you are ALWAYS in the middle of the enemy team during teamfights.
Most of the other items are self explanitory. Your fifth and/or sixth item should be abyssal or deathcap in my opinion so that the enemy team cannot afford to ignore you. There was a game where I built full tanky so no one focussed me so I ended building a deathcap. We had a teamfight where our carries were focussed and I was left against four damaged enemies. With my tankiness and damage from deathcap, I was able to get the quadra to prevent us from losing right then and there. We ended up winning that game. :D Anyway, I hope this was able to help you.