After Snowball is betrayed and chased off the farm by Napoleon, his name becomes synonymous with disaster and failure.
Specifically, Snowball is blamed for the destruction of the windmill as well as for breaking eggs, smashing windows, and plotting to attack the farm in collusion with the neighboring farmers.
Additionally, Snowball is eventually accused of fighting against the animals of the farm during the "Battle of the Cowshed", despite the fact that it was Snowball to planned the battle and led the animals during that fighting.
The specific accusations made against Snowball are, perhaps, less important than the way in which those accusations are made and the effect they have. Napoleon and Squealer offer no real proof that Snowball has been seen or that he has conspired against the animals of the farm. Instead, Napoleon and Squealer take advantage of the fact that Snowball is gone and cannot defend himself against any accusations.
After he is gone, Napoleon uses him as a scapegoat, blaming him for everything that goes wrong on the farm.
For this reason, Snowball's name is easily twisted into a negative symbol used to excuse any failures made on the part of the regime (Napoleon's regime). Napoleon's position as an authority figure allows him to essentially construct truth out of lies. This is the most important idea behind Snowball's (ruined) reputation.
It is also alledged that Snowball is coming into the farm at night and wrecking havoc on the farm, like knocking over milk pails and breaking eggs and mixing seeds. Also, rumours start to circulate about Snowball being in an alliance with the farmers and was previously working with Jones.
Snowball gets blamed for the destuction of the windmill, although we, as readers, know it was because of the dreadful winds. Once Napolean declares Snowball as the destroyer of the windmill, he and the pigs start to cause mishaps around the farm during the night and then begin to blame Snowball on them. By doing this, the rest of the animals put all the blame onto Snowball whenever something goes wrong.