This is Fun!!!
I would structure this as an organized competition with a round-robin or double-elimination style advancement bracket. A single encounter about wrestling a muddy hog is going to result in the players simply attempting grapples until they succeed because that what they'll think they need to do. If there are multiple rounds they will have an opportunity to see how other competitors attempt the task.
Naturally you won't want to run a session where you are just narrating a bunch of NPC's grabbing dirty pigs, but having a few other competitors who are using different tactics might inspire your players to try new things.
Consider using intimidate to frighten the pig into suffering a CMD penalty, or driving the pig into some deeper mud where it'll have a harder time trying to get away. Maybe trying to grab the pig a certain way allows for better leverage. Grabbing the pig by the ears might cause the pig to struggle less because having some drunken farmer grab your ears hurts. Grabbing his tail might let you get dragged around by the pig and tire the thing out. Grabbing his leg and letting him struggle to get away and then tactically letting him go and trying again might result in a pig whose legs are worn out and is now slower. Players should be encouraged to use their skills in clever ways for small bonuses, maybe slight of hand or bluff allows you to jump the pig by surprise. Knowledge (nature) or handle animal will probably provide insight into how to approach the pig or what part of it to try and grab. Sense motive to determine which direction the pig will try and run.
If there are enough competitors it will behoove the organizers to have several pigs as well. Different pigs may have slightly different stats, weaknesses or habits.
-This pig will charge you and deal 1D3 non-lethal
-This pig has a hairy butt and is easier to grab from behind
-This pig has stumpy legs and will get stuck in deep mud
-This pig is timid and will run when you get within 15 feet
-This pig is blessed, literally
Different pigs will succumb to different tactics and the players will be rewarded by leaning them
Since this is essentially a mini-game, try changing up other aspects of the game to make things seem more significant or interesting. Change the scale of the "combat area" to 3' squares rather than 5', and require DEX or acrobatics checks to move more than half your speed. Change the combat order so its more than "my turn", "your turn" style combat. The more different skills you can bring into the process the more you can expect your players to try different things.
Try this:
3' squares, players move half speed (typically 15'/5 squares). Movement is spent 1 square at a time, if more than 5 squares are covered the player sacrifices his (standard) action and makes a double move, or attempts dex/acro checks to move faster/farther. Unlike typical combat, the facing of "combatants" is important
A turn might look like this:
-Player starts by using any amount of this available movement to approach/circle the pig.
-During this move he/she may attempt a single skill check to gain an advantage over the pig, or to force the pig to move.
-The player makes a sense motive check to determine what the pig will do when attacked
ROLL INITIATIVE (if sense motive was very high maybe there's a bonus)
-any remaining movement is spent to lunge at the pig (dex/acro for extra movement), if the player won initiative their movement occurs before the pig has a chance to react and they may attack/grapple normally. If the pig won initiative it readies an action to run away if approached and thus its movement is simultaneous with the lunge from the player. This is where the sense motive really comes in, if it was successful the player has lunged in the correct direction and still has a change to grab the pig (though probably at a penalty), otherwise the pig squirms out of the way and the player gets a face full of mud (or more likely manure).
-if an attack is not made the player may move again/make a skill check as above. Some checks like determining a weakness or habit won't need to be renewed, while others like bluff/stealth for an advantageous position, or intimidate to make the pig run must be attempted again if their bonuses are to be kept
-repeat every round
-anyone who takes a full round action in the mud must make checks vs fatigue (players with endurance get a bonus), but since the pig will generally only take a single move to get away players must force the pig to double move or escape grapple for the pig to tire. Deeper areas of mud might increase this check, or even force escape checks. Fatigue here might mean lesser penalties (like -1 on str based checks, or -1 move) so that a single failure doesn't knock the player out of contention, but rather the fatigue will stack up until the penalties become to much. Making skill checks do not count as taking action for this purpose unless those checks require movement, so a player may move two squares, intimidate, move two more squares (for a total of only 4 out of 5 square single move), and intimidate again without getting tired out by the mud.
-you may also consider saves vs sickened for a mouth full of pig poop.
You can make this process even more interesting by adding some racially significant options, dwarves aren't slowed by the mud, halflings and gnomes may attempt ride checks, elves get a bonus to try and move faster in the mud etc.
Furthermore, if each round is against not only the pig, but also another competitor rather than a timed event there can be even more complication. Competitors can take action against each other, or lay in wait for their opponent to scare the pig to them. Randomly determined brackets can see players facing off against each other, or against a local NPC rival.
There is also the behind the scenes actions to consider. Judges can be bribed, competitors can get drugged, spells can be secretly cast, someone went and put a rage potion into the slop trough of pig #3!
