A forensic search of his phone identified 285 images and 21 video files of child sexual abuse dating back to 2018, including 50 classified as the most extreme category of abuse.
In his appeal this month Snell claimed he had access to, but did not distribute the material, and therefore shouldn't have been judged on it.
Defence lawyer Julie-Anne Kincade QC told the court Snell's case wasn't as severe as other cases and the starting point should have been two years.
She argued that Snell's otherwise good character and rehabilitative progress meant a sentence of home detention should have been awarded.
But Crown prosecutor Thomas Riley said the starting point appropriately reflected the seriousness of the offending.
"The term of possession was at least one year nine months. He had the opportunity to delete the material every day and chose not to," Riley said.
"In Snell's own words, he took comfort in knowing that the material was hidden there for his use if he ever needed."
In Snell's original sentencing Judge McNaughton described the offending as a "gross invasion of children's privacy".
He said Snell told a probation officer he had fantasies about sexually abusing the children he taught.
"In my judgment, your offending is extensive. "
In the High Court judgment, Justice Mathew Downs said Judge McNaughton was right not to award a discount for good character.
"For now, it is sufficient to observe Snell's offending did not involve an isolated fall from grace. That he thought sexually about some of his pupils underscores a distinctly aberrant mindset, and one anathema to his public responsibilities."
Justice Downs did however award Snell a discount for his rehabilitative efforts.
Snell's term of imprisonment started on July 13.
Where to get help
If you have concerns or suspicions about someone who may be trading in or producing child sexual abuse images or videos, contact Customs confidentially on 0800 WE PROTECT (0800 937 768) or Crimestoppers anonymously on 0800 555 111.
If you are, or know of, someone who is at risk or being abused, contact the police immediately.