There is a typical proceedure for starter rope repair, but if I know what engine you've got on your snowblower, I can tell you what tools you'll need as well and be able to give better step by step instructions. The engine will have its own model number separate from the snowblower model. Let me know what model number you find on the engine and I can walk you through the starter repair.
Ok, good enough. Some of the Tecumseh engines have little 1/4" screws that hold on the starter pulley housing, and others have that pulley housing riveted into the blower housing....if yours has the little screws in the housing where your rope winds up in, then that will be what you need to take off first. If not, then the whole blower housing(cover that goes over the flywheel) will need to come off to get at your starter pulley for rope replacement. The blower housing is usually held on by 3 or 4 3/8" or 7/16" bolts, and depending on how your engine is configured, you may have to remove the fuel tank as well. Once you have access to the starter pulley, you'll need to remove all of the old rope that is broken and remove the knot that was tied into the pulley end of the rope. Let me advise that you don't take the pulley apart unless you HAVE to as that spring can come flying out of there and be a real pain to get back in. Once you've got the old rope out, you'll need to rewind the spring that is underneath your pulley. Without disassembling, turn the pulley by hand holding pressure on it so it doens't get away from you. Turn until it is as tight as it will get and then back it off one full round. Hold pressure on the pulley and thread your new rope through the outer hole of the starter housing and then through the hole in the pulley. Once you've got it through the hole in the pulley tie a good knot in it and pull it tight from the other end. Slowly feed the rope into the starter housing allowing the tension that you just built up on the spring to pull it in. Slide your starter grip onto the loose end of the starter rope and knot it. Re-assemble the engine and you should be good to go. Please let me know if you need anything else.