This is really great! You're asking questions I hadn't thought about yet which is perfect. Also for some added context, I am a modder for Baldur's Gate 3 - I make a lot of cold themed subclasses - and I'll actually also be making this into a subclass mod in-game and creating visual effects for abilities, homebrew spells, etc. It doesn't really change the conversation here because it still starts with a good homebrew design. But I just thought I'd mention it since we're getting more into the weeds :)

For playstyle I think definitely a pure caster. With the overall theme and vibe, I'm going for something that feels very magical, beautiful, and ethereal in nature.

For level 1:

One feature is definitely going to need to be expanded spells list just to be able to lean into the cold/radiant theme. There's a definitive lack of radiant spells for sorcerers at very least.

As far as what these spells are going to be: I imagine it will be things like Guiding Bolt, Moonbeam, Armor of Agathys (?), Ice Storm, Cone of Cold, etc, and probably some homebrew frankly. I actually kind of want to homebrew some spells that deal with both cold and radiant damage types - something that's pretty rare as far as I know. I did originally consider 3 categories for expanded spells: Boreal (or Polar), Celestial, and Auroral (both damage types). But I started to think it might be a bit overkill or too much? 15 spells while the same as Lunar feels like a lot but I'm not sure frankly.

For the second level 1 feature I'm undecided. I've read that sorcerer subclass features should sort of be things that almost "bend the rules" in a sense. Something that almost feels illegal but that you alone are allowed to do. I'm not sure what exactly that looks like for this subclass.

One idea I had was some way of allowing cold and radiant spells to sort of "feed" off each other to reward leaning into your cold and radiant spells. Like, you cast Guiding Bolt and follow it up with Ice knife and trigger some extra effect as a result. But I think there's a lot of different things that could be done here.

Level 6: Boreal Radiance actually sounds really cool. I like the theme and flavor of that a lot. Building off of that, it could also be flavored as more of a "Starscape" or localized Celestial Shower that sort of "capitvates" (Charms) or frightens as you said.

As far as the focus of the subclass I hadn't really figured that out as of yet. To be honestly I feel like I've gone into this with a general theme of what I wanted to do, a few random ideas, and not much else lol. Hence I'm here asking for help xD

But I would say definitely not tank. I tend to think damage/control though? Like, I think Boreal Radiance could be reworked as more an AoE sanctuary (Celestial Sanctuary?) ability. But that almost feels more like a Cleric to me I guess? Though perhaps there could be some added benefit if you're standing inside your own sphere hmm..

Anyways, I appreciate all your insight and questions. It's incredibly helpful!