Giants....

[Legate of Amon Lanc]

Possibly. This would be one explanation. The other is, that it would be Caradhras itself: if you take literally Gimli's (and Gandalf's, and whoever else might have said it) lines about "cruel Caradhras". It might be pure personification of the place, but it seems like something more. My thoughts come from these points in the text:

'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.'
'It matters little who is the enemy, if we cannot beat off his attack; said Gandalf.

Thus, why I think it is Caradhras itself:
1. Aragorn calls it the wind, though he agrees that it is this "wind" what is evil here. It would seem to me as weather around the Caradhras, being something like a part of it.
2. Aragorn speaks about things, which have little love for those that go on two legs. If I am not very much mistaken, then Giants have two legs, then why would they hate everyone who walks two legs. It might be a metaphore that they just hate all living, but why would then Aragorn use such a stupid metaphore, when the Giants have two legs as well.
3. Gandalf has on his own eyes seen Giants (in the Hobbit) and he spoke about them to Dwarves and to Beorn, but he seems reluctant in naming the enemy now (unless he just doesn't want to talk about nonsenses while there are more important things to do). It seems to me that Gandalf does not know who the enemy is, or that it is something he does not want to talk about.

And to end this, for illustration just more quotes from Gimli, which may take Caradhras just as a personification, but also might consider Caradhras as true entity:

'Caradhras has not forgiven us.' he said. 'He has more snow yet to fling at us, if we go on.'
(...)
'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.'

It is true that it might be a "strange dwarven belief" (as is mentioned in Appendix A III, that the Dwarves "had many strange tales and beliefs"), and the fact that Boromir says to Gimli "But happily your Caradhras has forgotten that you have Men with you" (which seems to me like a little scoff) would somehow support that. But still, maybe Boromir was the one who didn't know everything about mountains.