さむいのはきらい is grammatical. But さむいがきらい is not.
You understand how のは/が is used with verbs, but it is used in the same way with i-adjectives and na-adjectives. The subject marker particle が must follow a noun or noun phrase. So さむいが is ungrammatical just like みるが is ungrammatical, and the problem is fixed in the same way, by nominalising the predicate.
As an aside, you can also change many i-adjectives into nouns by changing the final い to さ. This would turn cold into coldness. Then you could say さむさがきらい.
Another aside: I said that さむいがきらい is ungrammatical, but that is assuming that が is the subject particle. If が were the conjuctive particle, meaning 'but', then this would be perfectly grammatical and could mean something like "It's cold but I hate it."