I'm putting ariens hand warm grips on 836 John Deere snow blower and to know how to wire it. The motor is a 8hp Tecumseh.

Visit the on-line store, know as reliable-store, they have the repair manuals. I'm sure you will get the solution of your problem.
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Several engines were available, you need to look for the number on your current plug - easiest method.

otherwise, you will need to give the motor manufacturer and nameplate info (Tecumseh SnowKing 8HP?)

That would be a H50 engine. Here is a link to the service manual. Look in governor section and find your particular setup; there are several to chose from.

http://www.mymowerparts.com/pdf/Tecumseh-Service-and-Repair-Manuals/TECUMSEH-SERVICE--REPAIR-MANUAL-3HP-TO-11HP-4-CYCLE-L-HEAD-FLAT-HEAD-ENGINES-692509.pdf

OK the wire on a coil is to shut off motor when grounded, so if you don't hook it up it will not shut off when you try. That wire goes to throttle linkage so when you slow engine speed to minimum it shuts engine off. Most snow blowers that have the red safety key in shield have that same wire slit from the throttle so if that malfunctions you still have a safety shut down.

Does it have steering control triggers to turn it left or right...if so hold both at the same time with engine off and see if you can push it..Let me know if that works. Or let me know what kind of controls you have

Could be the belt is broke or come off or the pully loosened on the shaft. Good Luck

Look on the unit and find the model number. It usually starts wit 917.
Find it and then go to sears.com and type in the model number.

so what is the problem??

that could be wiring issue that the batter isn't able to take up the electricity supplied to it.. u know, the conductor between them..
if possible get a manual from reliable-store to fix it urself

Hi, You have gum or old gas in the main jet on the carb, turn your fuel off, stand the snowblower on the front blower housing with handles in the air, remove main jet from the bottom of the carb and clean. Jim