
Cheapy |

Summon Monster II will gain the cold descriptor thus making it a valid target for Rime Spell.
The ice elemental will not make the target be entangled, since the ice elemental is not the spell. Similarly, if you are invisible and the ice elemental attacks a creature, you will not become revealed, as your spell didn't attack the creature, but the elemental did.
So what does Rime Spell do for Summon Monster II? Raises the spell level 1 by and possibly makes casting it a full-round action, but nothing else.
It's all for naught though, since ice elementals aren't valid creatures for Summon Monster.