Nice photos. The snowblower looks to be in great shape.
The fuel shut-off seems to have been removed. No big deal, they sometimes break anyway.
The previous owner installed an in-line fuel filter (see the reddish brown plastic circular button that the fuel line passes through.
If the carburetor is not getting gas:
1) start first by removing the fuel line from the fuel pump where it goes into the carburetor. If when you turn the engine over you don't see or smell gas there, put the line back on. If you do see gas coming out of the line go to number 4 below and see if the carb is gummed up.
2) Next remove the little reddish brown fuel filter from the lower side (not the gas tank side) and see if gas is flowing through the filter. These inline filters are normally a good idea. But with a fuel pump on the gas line they can be problematic. Still, they should not prevent the carb from getting enough fuel to run.
3) Prime the fuel pump. I took mine off and soaked it in a pint of gasoline over night. After that I put it back on and it never gave me a problem. Aftermarket part and diaphrams are posted on this web site. If the real thing is going to blow your budget.
4) really clean the carburetor (not just the bowl). This was the solution for me : The two (2) pages on this link should be all you need
http://www.opeonthenet.com/phpBB2/viewtopic.php?f=1&t=6676&hilit=yamaha+carburetor