Despite the fact that both of his sons have demonstrated the ability to transform, King Cold is never shown transforming in the series, though the Dragon Book states that he appears as the type who would be able to transform.

Is King Cold stronger than Frieza?

26 Stronger: King Cold

The fact that Frieza, one of the most tyrannical characters, actually obeys King Cold is very telling. ... However, there is nothing conclusive to say that King Cold is stronger. If Frieza really was stronger, he would've usurped the position of king from his father a long time ago.

How many transformations does King Cold have?

Transformation: This is King Cold's ability to morph himself from a weaker state to a more powerful one. In all, Cold, like his sons, Frost and Frieza, demonstrated three transformations.