As Parker repeatedly asks after they bring the face-hugged Kane aboard, why don't they freeze him? I understand that Ash doesn't want to, but neither Dallas nor any other crew member provide any reason for not putting Kane in cryo and dealing with him later.
This is dealt with in the script.
Ash is the ship's Science Officer (and Medical Officer pro tem). Although the other crew express concern towards their fallen comrade, none of them actively dispute that Ash has the right to make decisions regarding Kane's health and well-being. This point is repeatedly made in the scenes before Kane dies.
DALLAS : (to Ash) You're the science officer. It's your decision.
RIPLEY : How could you leave that kind of decision to him?
DALLAS : I just run the ship. Anything that has to do with science division, Ash has the final word.
The novelisation makes it clear that the cryotube doesn't create a perfect stasis (a la Star Trek) but functions as a suspended animation device, slowing the user's vital signs but not stopping them. Entering in an unwell state might delay your death but it certainly wouldn't stop it.
Ash claims that Kane needs immediate medical attention and then (once he's stabilised) presumably they'll consider placing him back into stasis with the rest of the crew for the return journey to Earth. Obviously the reality is that Ash is a damned liar but we don't find that out until later...
ASH : Running a fever. And still unconscious. The machine will bring his temperature down. His vital functions are strong ... who knows, he may make it.