Can I run a Mud tire up front and an All Terrain in back or is it best to keep all 4 the same style?

IMO, on a 4x4 you should run identical tires (same size, same brand, same tread) on all 4 corners. 
Why would you want to run ATs on the rear and MTs on the front?  Sounds like that would be ass-backwards.  I would want the "better" traction tires on the rear (if I was going to mix tire types...which I wouldn't).

As long as you're not planning to use it in 4WD, you can run whatever tire you want, wherever you want.

If you're planning to use 4WD, I would strongly suggest all four tires be the same size, and preferably brand, type & condition - although to be honest, if you're on a low traction surface where 4WD is needed, it doesn't make that much of a difference.

The problem is drive train "wind-up" - if you operate a part time 4WD system with different sized wheels front & back, you run the risk of having the drive train bind because the front is turning at one speed whilst the rear is turning at another - this is the reason you don't use 4WD in a part time 4WD system on a hard surface, the first turn will have the front end travelling further than the rear end.

If you use different sized tires, you will subject the drive train to unnecessary stress - on a slippery surface the tires will slip and allow the stress to dissipate, but the firmer the surface is, the more the stress will build - definitely not an ideal situation.

ya, I was upset about no road hazard warranty on my Nexen M/T's and have 2 A/T tires but I feel better today so I'll pay the close to $200 for the tire.  Been a while since I bought them so the sticker shock always stings

I ran the same tread style but different brands before but that was temporary and on a 2 wheel drive truck

thanks

I'm currently running 215-70-15s on my Samurai.  When I got the thing from my father-in-law, it needed two new tires, and that was all I could afford.  I put the new ones on the front.  They are the same size as the rears, but a different mfgr and a different tread pattern.  I currently run 22 psi up front and 24 psi in back.

I drive 99% on-road, and only use 4wd in snow.  But I was wondering if it might be a better plan to put matched tires on LF and LR, and RF and RR.  In theory, there would be no front-to-rear difference, and the axle diffs would handle any small difference between left and right, just like going around a curve.

Am I insane?

(I know that the real answer is to get 5 matching tires and rotate regularly, but economics will not allow that right now.)

REMEMBER YOU SAID IT !!!LMAO