Hi! Wondering if I can, theoretically, freeze a neon tube inside a block of ice? Obviously the electrodes would need to be outside of said ice block and insulated. Excited to hear feedback on this one!--

Yep. You can freeze electrodes too (ask me how I know) 

https://expressional.social/@JamesAkers/116347171820905000

Dale Chihuly once froze a bunch of neon, so some friends an I wanted to do it to in an ice melting, glassblowing performative context.

We used helium so it would melt the ice more. An I used some controllable tech 22s to have fun with some audience interaction elements. I also had an argon mercury tube. 

Good to make sure the bends are nice in the tubing before you freeze em in. Its a bummer when they crack. Interestingly they can sometimes half work when broken but half frozen- water IS conductive. 

I would use transformers with safety's. It feels a little weird to have the water and the electricity together. No one was electrically shocked during our little performance though. 

Regarding electricity and water-- you can run neon tubing underwater-- if the electrode boots are suitably insulated.  In the late 80s, a company was marketing fully waterproof boots and caps and at their NESA convention booth, they had neon units running inside a fish tank while goldfish happily swam around and you could put your hand in the tank as well.  I did not get shocked, and to my knowledge, neither did anyone else.

Also, as an aside, deionized water is non-conductive!  It is used in applications such as cooling large electron tubes where the plate forms part of the envelope and it is put into a water jacket with circulating pumps for cooling.....this was once commonplace in radio stations.  But, ANY contamination of the D-I water will make it conductive again, so you'd never be able to put your hand in it.  But its one of those interesting tidbits that people find hard to believe when you tell them that there is water that won't conduct electricity.