Unless rats are somewhat peculiar by mammalian standards, being in a confined space with dry ice is probably an ugly way to go. Sensing lack of oxygen is something that most animals(and people, which is why inert gas asphyxiation or carbon monoxide poisoning are so often lethal even in situations where the victim could have easily left for some fresh air if they had just been aware of the problem) aren’t very good at; but elevated CO2 in the blood will trigger reflexive attempts to correct the problem; which will obviously be futile and increasingly desperate in a CO2 atmosphere.
The rat would still succumb to lack of oxygen markedly faster than to the alternatives of mechanical trauma, poison, dehydration, etc. but they will likely not be happy about it. Nitrogen they would probably barely notice. Unfortunately, liquid nitrogen is a bit more of a pain to handle than dry ice is.
