People are generally in a good mood during late December. It is the best time to send a 'Year-End Update' message.
Template for Alumni:
'Hi [Name], hope you're having a great holiday season. I just wanted to update you that I've finished my 3rd year and learned [Skill] based on your advice last time. Thanks for your guidance. Wishing you a happy new year!'
Notice there is no ask. You aren't asking for a job. You are building a relationship. When job openings come in January, they will remember you.