In the book, Caradhras is not shown to be sentient. Whether it is merely a natural location where the weather is particularly bad or there is a supernatural force behind this is left unsaid. I think this is deliberate: the world is one where supernatural beings do exist (if trees walk, why not mountains?), and a hostile presence is a conceivable explanation, unlike weather patterns based on fluid mechanics.
In the movie, Saruman is shown to speak to Caradhras, but this does not happen in the book.
Caradhras is introduced in these terms (LOTR II.3):
Yonder stands Barazinbar, the Redhorn, cruel Caradhras
A few pages later the party comes into sight of the mountain:
On the third morning Caradhras rose before them, a mighty peak, tipped with snow like silver, but with sheer naked sides, dull red as if stained with blood.
There was a black look in the sky, and the sun was wan. The wind had gone now round to the north-east. Gandalf snuffed the air and looked back.
’Winter deepens behind us,’ he said quietly to Aragorn. ‘The heights away north are whiter than they were; snow is lying far down their shoulders. Tonight we shall be on our way high up towards the Redhorn Gate. We may well be seen by watchers on that narrow path, and waylaid by some evil; but the weather may prove a more deadly enemy than any.’
The setting is ominous (there are other negative signs, such as a flock of black crows). There are possibly monsters living in the mountains, but in Gandalf's words, the deadly enemy is the weather. The opinion of the party is divided:
‘We cannot go further tonight,' said Boromir. `Let those call it the wind who will; there are fell voices on the air; and these stones are aimed at us.’
‘I do call it the wind,’ said Aragorn. ‘But that does not make what you say
untrue. There are many evil and unfriendly things in the world that have little
love for those that go on two legs, and yet are not in league with Sauron, but
have purposes of their own. Some have been in this world longer than he.’
‘Caradhras was called the Cruel, and had an ill name, said Gimli, `long years ago, when rumour of Sauron had not been heard in these lands.’
‘Caradhras has not forgiven us.’ he said. ‘He has more snow yet to fling at us, if we go on. The sooner we go back and down the better.’
The party is snowed in. Legolas goes scouting:
‘They despaired, until I returned and told them that the drift was little wider than a wall. And on the other side the snow suddenly grows less, while further down it is no more than a white coverlet to cool a hobbit's toes.’
‘Ah, it is as I said,’ growled Gimli. ‘It was no ordinary storm. It is the ill will of Caradhras. He does not love Elves and Dwarves, and that drift was laid to cut off our escape.’
So the place where the Fellowship is is hit particularly hard by snow. This could be due to some malevolent entity controlling the weather, or it could be a natural weather pattern — mountains have sudden, extreme weather events that can be surprising to plains dwellers.
And indeed with that last stroke the malice of the mountain seemed to be expended, as if Caradhras was satisfied that the invaders had been beaten off and would not dare to return. The threat of snow lifted; the clouds began to break and the light grew broader.
“As if” Caradhras was sentient — which isn't to say that he is.