The blower won't throw snow - especially heavy snow. Auger and impeller turn but bog down. Trying to replace belts, but there are no numbers or sizes on them. Are these generally available (say at a NAPA store) or do I need some special Ariens belts?

I take it that you have a 2-stage snow blower, that is is has the auger blades and then the 2-stage impeller. The impeller blade is damaged <<OR>> the motor is to small to through the snow far. If you have a 5-horse engine and throwing heavy snow, the snow may not go as far as the light fluffy stuff.
A single stage snow thrower is not designed to throw snow far, just move it over a bit.

You should check for belt condition and adjustment. Under more load the auger/impeller belt might start to slip and would result in poor performance. For improved performance in wet slush there is an "impeller modification" that can be found with a web search. It's adding rubber wipers to the impeller blades and it does a great job of tossing that stuff out the chute instead of clogging it.

Check the auger shear pins replace if necessary with correct parts(not regular bolts).
If auger and the impeller are not turning your cable is out of adjustment.
If only the auger doesn't turn, and the shear pins are ok then the brass/bronze gear has shredded which is why proper shear pins must be used. Donyboy73 on youtube show how to replace that gear on an older but similar MTD affiliated blower.

the auger and impeller are geared to work together. the auger does turn much slower then the impeller. You may not have a problem at all

I am going to assume the belt is good if the impeller it running. You can check the belt by removing the plastic cover in the center of the snow blower.
With the unit safely turned off reach in and turn the blower by hand while putting a little resistance with your other hand on the impeller. Does the shaft from the impeller to the gear box turn?
Does the shaft that the augers are attached to turn? If the impeller shaft turns but the auger shaft doesn't, the gearbox in the front is bad and will have to be replaced.
I the auger shaft turns, check your shear pins again. Sometimes they will break but still stay stuck in the holes. Actually take one out and check it.
If it is a Craftsman you can get a manual from managemyhome.com and parts from searspartsdirect.com. You will need the model number of the snowblower. The number looks like 247.123456.
Any other questions please ask. Do't forget to rate this answer!

I have a toro 98 cc powerlite snowblower model 38182 it was running fine one day then bog down and died after that i cant get it to start it has a good fire on the plug plug isnt very wet it pops threw carb once in a while help

does the impeller spin and not the augers.if so check sheer bolts.if neither impeller or auger spins check auger belt.

On one side of your machine you will find a cover that you can remove, the belt for the auger is in there. From what I can see there is no adjustment. Check to see how the belt looks.If it's chewed up it will need to be replaced.If you remove the belt try to turn the impeler to see if it turns freely, if it doesn't then check to see if there is something wedged. if nothing is wedged and the belt is off and it still don't turn by hand it could posibly be a bad bearing.if it does turn by hand. Also check the belt pulleies to see if they are ok, the only pulley that will sshould spin freely is the idler pulley, the one on the engine shaft should spin the moter so make sure you pull the spark plug wire off to check that one, and the auger pulley should spin with the auger.

the problem could be the snow is to heavy for the motor to keep up, if thats the case you may need to upgrade to a more powerful model or try not to overload it. take it a little slower so the motor can keep up. but try tightening the belt. with your pointer finger push down on the belt it should have about a half inch give, if it moves more than that its too loose and probably slipping under load