Service light stay on when driving it misses bad

Could be spark or fuel.
Weak or worn spark plugs, weak coil, dirty injector, and so on.

Go to an auto parts store and have them scan for a code. That should give you an indication of what is wrong with it.

have a load test done on the battery as it may be failing and not providing sufficient power to run the ECM. Check for alternator drive belt condition and tension. The combination of low current out put from the alternator and bad battery especially in cold weather will cause problems as describe.

I'm not a mechanic but from experience I suggest that before you start with repairs, start with the fuel. You may have either picked up some dirty gas when last filled up or just stirred something up in the tank. Try a fuel cleaner from any auto parts store. Also, and this is probably not realated, the check engine light may come on if your gas cap is not tight. Good Luck

Is the check engine light on ?
The engine could have a slight miss-fire which would be made worse by the load of the a/c.

The miss does not vanish, the noice gets cammouflagged by the noice of the engine. Check service engine light first, Auto Zone or Advance will do it for free. Then post again with your engine code.

you can start by going to Advance Auto they will scan it for free and tell you what the code is and that will give you a good starting point but in my dealings with the PT they are hard on plugs and wires so a good old fashion tune up is probably all it needs. I hope this helps you.

Most likely the intake gaskets are bad. they will sag in the middle over time and allow a vacuum leak between the head and intake. recommend replacing the gaskets with the steel instead of plastic ones.

I also have this exact truck and I am a drivability technician.
First if you have a dead miss check for waht code is stored. Even if the light is off a code should still be stored. Once you know what cylinder is missing you can rotate the coil and and see if the miss follows by checking codes again. Do the same for the injector even tho this is alot more work. Once you determine that the code always stays on the same cylinder then you can inspect for maybe an intake vacuum leak or if the EGR is close by sometimes a EGR stuck open will miss at low RPMS. Its suppose to be open when cruising so a miss would not occur then.

Why was the engine work done. maybe you didnt fix the pryor problem if you didnt have the head sent out to be inspected and block tested. These engiinee heads are known to fail with cracks thats why it needed to be tested. Hopefully you did this

Take it back to where you had it serviced. They probably simply missed connecting the fuel level sensor. The engine light is probably from a missed emissions hose that goes to the gas tank.