Lmao Spike, careful now. It would be some nice tension if Spike was cold long enough that he started feeling sleepy. Specter would probably realize his friend might be in physical danger (Spike showing symptoms of hypothermia) but then Spike pushes through anyways and they manage to complete their mission just moments before Spike goes unconscious and needs to be warmed up. Only question would be: How Pink would feel about the situation if this happened?

The internal drama loving part of my brain is screaming in agreement with you! Unfortunately it takes a different route that I need Spike conscious for but it kills me because that's good delicious drama!

Though in the alternate universe where that event happens I think Pink would be.... not entirely upset that it happened to Spike because Pink really has no love for humans, but upset that it would easily be getting her into big trouble. Even if Specter and Spike aren't in a relationship yet, this scenario is just a bit before it officially happens in-story, in a hypothermia route it could push that up ahead and boost their relationship sooner, but even if it didn't Spike is still Specter's personal "Pet" at this point and so Specter directly would be pissed at Pink, which she would hate much more than whatever happens to Spike.
She's not entirely a careless sociopath, but has only been back in the story a short period of time and so with her default dislike of humans Spike hasn't had enough time with her to really earn his place with her (That is what the entire scenario with going to the park is about; Earning him a positive relationship with Pink)
If the Hypothermia route DID happen AND Pink realized all the work he went through to replace her ruined box she would probably feel bad, but it would be overridden by getting pissed about getting in trouble with Specter.
(Damn so many optional routes! Like a VN game!)

lol yeah
Hypothermia can be genuinely dangerous if allowed for too long. The body dropping temperature even by a few can damage more sensitive organs. If too cold you could start losing the tip of your nose, parts or the whole ear, fingers, toes, etc to frostbite. In this situation it likely would not mean anything longterm for Spike, but imagine if he was left cold for too long and Specter was forced to face the situation that is friend/soon-to-be-lover has a mortality that is rarely seen. He probably would not die in this situation but it would definitely be a situation with stakes.

My heart desires to place that level of amazing drama thre but the other half of my brain is saving that kind of drama for violence near the end of the story D:
God I wish I could write like I was 11 years old again where every chapter was just the same life endangering escalating danger where characters where crying over eachother swearing their love and vengeance over and over again! It would feed a need in me!