First, what model of tractor are you mounting it on?
The speed-up pulley is not a factory modification, and the clutch does not change. All of the mechanical PTOs are the same diameter.
I have always run 1/2" belts on my snowthrower tractors, as the aftermarket pulley that matches the original one is a 1/2". Since you no longer have the OEM pulley on it, you'll have to measure for the correct size belt. And at any rate, the only way anyone is going to know if the belt your thrower came with is actually going to work or not would be for you to put it on and try it. We have no idea what size pulley you now have on the snowthrower, so you'll have to measure it and buy the appropriate belt. A 3/8" belt will bottom out in a 1/2" pulley and not work.
Also, if the pulley is die cast aluminum, don't use it. You need a stamped steel or cast iron pulley.
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