I am planning to get a set of Mud Tire for my JK.

The size would be 33 inch for sure because I want to keep stock suspension
and just install Xenon Fender flare to clear the wheel well area.

But now I am facing choices of width of tire. I can choose 10 inch wide tire
and keep my stock rim or I can go with the common 12.5 inch width.

Can anybody tell me how important the tire width would be for offroad?
My area is mainly mud.

 

From what I have seen and done if your in mud than narrow and tall tires work better. If you not going to and spacers than you will have some rubbing.

 

A skinnier tire is probably a tad bit better in mud, but IMO wider tires look much better... I don't know if that really matters to you though..

Also, you can run 35's on a stock suspension w/ the flares and a 1" body lift which would not affect your suspension.

 

Traditionally, mud tires were tall relative narrow, with square shoulders and high void ratio tread.
They were designed to cut through the soft mud, down to solid surface to gain traction.
The blocks on square shoulders facilitated the cutting, while the high void ratio was designed to be self cleaning.
A narrower tire obviously had less mud to fling to get to a solid surface.

The current trend is to use wider mud tires, probably not because they are better in mud per se,
but because they are a better all around tire on rocks, mud, sand and appearance.
The tradeoff is that wider have a lot more mud to fling and will tend to float.

 

it really does make a lot of difference in my experience (i live in southern mississippi, so my jeep is typically a nice a mud brown color), as for your size, personally i liked my stock rubicon wheels so i used Spidertrax spacers for side clearance, i have the 33x12.50 MT Baja Claws, I SHOULD have went straight to 35's though... using only a 2in SkyJacker BB kit, I have plenty of clearance for 35's. 33's work fine but the 35's would have fit without problems. In short for less then your spare tire cost's you can maintain your stock shocks and springs and keep your cool looking factory wheels and run 35x12.50s.