if Red Skull was not teleported; am not sure about either character becoming frozen for any length of time.

only way for Red Skull to also become frozen might have been if there was any means to restrain him. if I recall correctly, there was not.

If they find red skull in ICE they would keep him in ice

He would be kept on ice unless someone like Zola found out and was able to unfreeze him

This would have lead Red Skull to be one of the antagonists of an Avengers movie

Plus by the time of Infinity War someone else would have been the guardian of the Soul Stone