That whole 'ice monster romance' thing made me think of 'Beauty and the Beast' retellings, but frostier. The most direct fit has to be Regine Abel's 'I Married a...' series—'I Married a Lizardman' isn't ice, but the worldbuilding treats 'monsters' as just another species. For something colder, 'Winter King' by C.L. Wilson is a stretch; the hero isn't a monster, but his magic is winter-based and he's seen as monstrous. The vibe is there.
Honestly, the monster romance subgenre leans heavily toward scaly, furry, or tentacled, not crystalline or frosty. You might have more luck looking at alien romances with arctic homeworlds, like in Ruby Dixon's 'Ice Planet Barbarians' spin-offs. The males aren't ice monsters per se, but the setting is brutally cold and they're often portrayed as primal and dangerous.
Finding a true romance from the POV of a sentient ice elemental or golem is surprisingly niche. LitRPG sometimes has ice-attribute protagonists, but the romance is often secondary.