The mountain the Fellowship attempted to cross via the Redhorn Pass was Caradhras. It is one of the three great peaks surrounding Dimrill Dale in the Misty Mountains, alongside Celebdil and Fanuidhol.
Caradhras is the Sindarin name for the peak; its Khuzdul name is Barazinbar. The Redhorn Pass crosses the mountains near its slopes and was a dangerous route even before the Fellowship arrived. Heavy snow and an unnatural-seeming storm forced the travellers to abandon the attempt.
The Fellowship then chose the West-gate of Moria, entering the ancient Dwarf-realm through the Doors of Durin. Caradhras is therefore easy to confuse with Celebdil, also called Silvertine, beneath which Moria’s mines were established. The mountain’s hostility is also connected to the Balrog’s presence deep below Moria, though Tolkien leaves the precise cause of the storm open to interpretation.