In 4th ed I played an ice maga, despite (or maybe even precisly because) ice and cold was so poorly defined.
We used reasonable (to us) interpretations and governed that ice is water in another form, Terram (despite being used in some 4th ed ice spells) is not needed for solidity. And Ignem was not needed as a requisite, unless you wanted the ice to not melt even if it was warm enough to. Surrounding someone or something with ice would chill them/it but for true cooling or freezing we'd use PeIg. And PeIg would be used to freeze water. Back them it was not clear (at least to us) that ReAq could change water from fluid to solid. If anything we thought it used Muto. But Terram was never, ever used. Sure, some PeTe or Re Te spells could destroy or move solid things, and we allowed them to work, using casting requisites. It worked fine for many years.
In 5th ed I think ice is even more clearly defined as Aquam, I have never been in doubt. And Rego is clearly (to me) used to change water into either steam or ice. I still see no need for Terram, and feel the same way about chilling people or things. And I still think PeIg could freeze water. There are more than one ways to skin a cat.
As for lava, my current saga has a magus with Elementalism using this gimmick. Our interpretation is:
Magic involving lava, such as creating is with Creo Terram (lava is rock, rock can naturally be a liquid, just as water can naturally be ice), has an Ignem Requisite (no added maginitude as it's necessary). Use guidelines for damage as for Creo Ignem (i.e. at Voice Range damage is [level-5]. Resistance is versus a Terram effect not Ignem, because otherwise what is the point?Using a Creo Terrem (Ignem) spell rather than just Creo Ignem needs to have some benefit. Resistance Mastery and similar spells for Ignem spells, Pilum of Fire etc is not useful as they only cover fire not hot lava. Ward Against Heat & Flames gives a Soak bonus vs lava, because it protects against heat. Soak is modified by Ignem Form bonus because the heat of the lava is the most dangerous part. Exempli Gratia: "Pilum of Lava" CrTe(Ig) 20, Voice/Mom/Ind, dam +15.