How can I tell if it is my tires or transmission burning smell when stuck in mud

Question edited for clarity.
Question moved to model category.

Try cleaning the Throttle Body and MAF (mass air flow sensor). If that doesn't fix it, an auto electrician with a pro grade scan tool computer can diagnose which sensor is causing it to dump fuel in 'Short Term Fuel Trim'.

Videos for both jobs below.

Pull it out have someone driving the Kubota at the same time

When you "let the clutch out" I'm assuming that you are removing your foot from the clutch pedal. That essentially connects the transmission to the engine.
The vehicle will not roll for several possible reasons:
1) The transmission is in gear and the engine is not running.
2) The parking brake is ON.
3) The brake pedal is depressed.
4) The brake shoes (or pads) are stuck or rusted to the drums or rotors.
5) It is still sitting on blocks
6) It has 4 flat tires
7) It is stuck in a mud bog

You can't use 4 wheel on dry or even wet pavement. It must be snow dirt gravel or mud. Pavement will just burn up your tires because the front Axel pulls faster than the rear. When you have good grip there is a friction fight between front and rear tires.

Does the smell happen while the car is moving, or will it do it parked ?
Is it coming thru the vents ? Can you tell if its from the engine compartment ?

sound like transmission got too hot.if you try for a long period of time keep spinning tires trying get out of mud you will burn out transmission bands and drive forward friction plates.when stuck in mud or snow dont keep spinning tires for traction will burn out transmission.

You will need to check where the liquid is coming from, It may be anything from Air Con, Fuel, Transmission Fluid etc..

The fact you smell burning plastic could be 3 things..

1, Brake pads could smell and burn down if they are on too tight (Had this problem with a trailer). Hence when you apply the brakes it could be squirting brake fluid out due to too much pressure.
- Check brake fluid

2, If the smell and liquid is inside the car (front pass side) it could be the air ducts. Under the dashboard you have air ducts etc for the fans and in car cooling (brother had issue with this)

3, Whatever the fluid is, it could possibly drip onto something hot, unusual for liquid to smell like plastic though, Auto transmission oil smells like fish.

Best bet would be the brakes. Next time you smell it just smell in the wheel mag and see if you can smell it, check the engine fluids often and dont use A/C (Air Con) as that does drip fluid (normal). If it is the brakes smelling you will need to have the lines bled out, tyre places may be able to do this, and possibly new brake pads

Good luck

Park on level. Put transmission in neutral, emergency brake on, and block or chock a rear tire, so car won't move when you raise that front tire with a jack. Use a jackstand or big block to stabilize car (safety first!), when it's raised.
Now try to spin tire. If caliper is stuck tire will be very difficult to rotate.
Found the problem yet? Take the wheel off and investigate further. The burning smell has to come from somewhere. Any sign of brake fluid leaking?
Have somone pump the brake while you watch the caliper. You should see a very slight movement when caliper pushes pads against the brake rotor. When brake is held, the rotor should not turn. If it does, the caliper is stuck inside the bore, and will have to come off for rebuild or replacement.
Good luck.
Hope you find the problem,

1. A stuck brake caliper piston causing the brake pads to ride on the rotors while car is in motion.
2. Improper hand brake adjustment will cause the rear caliper to hook up even if the lever is all the way down.
3. Manual transmission operates with a semi-metallic clutch disc similar to brake pads can produce similar odor when you ride on your clutch pedal.
   
4. You could also be riding on your brake pedal while you operate your vehicle.
5. Last but not least, you might have run over plastic debris and stuck on your exhaust pipe melting in the process.

This are common sources of burning rubber which people mistaken think their tires are burning. The only way you can burn your tires is if you do wheel spins, high speed braking and locking up your wheels and setting it on fire.

1. How long was it stuck in the mud, and 2.how deep was the mud? 3.Did you spin the tires like crazy for a while trying to get out? 4.What happens when you put it in gear and give it gas, does the engine speed increase, but the car just won't move?
If you (or someone else) beat the heck out of the car trying to get unstuck, jamming it in drive and reverse quickly, you may have blown the transmission. If the car sat in the mud for a while (a week or more?), the brakes might be the issue. You can check to see if it's a brake issue by starting the car, put in neutral, and have someone try to pull it with a tow strap or chain. If it won't move, or it does but the wheels don't roll, it's the brakes. If the wheels roll, it's the transmission. Check the trans. fluid level also. It's possible it's just low and won't engage. Let me know what you find.