This is how you'd wire things up (forgive my lack of artistic skill with MS Paint)

https://imgur.com/6uAG48L

You need a fairly chunky bridge rectifier, perhaps this:

https://www.amazon.com/NTE-Electronics-NTE5322-Rectifier-Recurrent/dp/B0002FRBZ0

which, although bigger than necessary has the advantage that it's got spade terminals which makes wiring possibly easier for you.

You need a diode to ensure that the relay only fires when the direction switch on the snow blower is in one position, like this:

https://www.amazon.com/NTE-Electronics-1N4007-Standard-Rectifier/dp/B008UG15QY

You only need one, but this is the smallest pack size I could readily find on Amazon

You need a 36v coil relay with DPCO contacts, perhaps like this:

https://www.amazon.com/Baomain-General-Purpose-terminal-PTF08A/dp/B01IMPE85M

You can forego the plug-in base if you want to solder wires directly to the pins, which would save space / weight and improve reliability but isn't necessary.

Depending on which way round you wire the diode (cathode up or cathode down) will determine direction of rotation of the motor. What this means in real terms is wire it up, and if the motor is switched to run in the wrong direction, you can either swap the wires going to the motor from the relay, or invert the diode.