My comments/critique in bold!
Name: Coldrain (Coldkit, Coldpaw)
That's an interesting name, definitely original
Age: 34 moons (52 at death)
Age is good
Appearance: Small black tom with white underbelly, chest, muzzle, and toes. Has a black marking on his chest that looks similar to a raindrop. He is lean with long legs and medium length fur. He has golden-amber eyes. He also has a y shaped nick in his right ear and a long scar across his belly.
Wow! Really descriptive and you included scars which all wild cats have unless they have never been in a battle. Realistic too!
Nice, there seems to be a lack of toms in the warriors world.
Personality: Coldrain is a very nervous cat, ears constantly pricked, he is anxious alert and rather skittish and is often self doubtful but despite that he is also very good at making other cats feel better about themselves and can be very loving and compassionate. He would die for his mate and can be overly suspicious of others sometimes
Its good but how can he be self doubtful but good at making other cats feel better about themselves. Self doubtful suggested that he had low self esteem but wouldn't that mean he's not the greatest at making other cats feel better about themselves?
Strengths: he is a good swimmer and great tree climber. He is also a hard-worker. He has very accurate hearing, too.
Sounds good and realistic
Weaknesses/Flaws: He is scared of larger toms which leads him into being a clumsy fighter. In no way does he excel in socialising. He hates hot days since his black fur gets really hot.
The bad at socialising corresponds with being so nervous. His strengths and weaknesses seem pretty balanced
Clan: TorrentClan (my Clan) or ShadowClan (canon)
TorrentClan is a cool name, I get the swimming part now. ShadowClan is cool too.
Backstory: As an apprentice he was given Eagletalon as his mentor. This mentor of his would severely overwork him, giving him harsh punishments whenever he made mistakes. Over moons, he built up Coldrain's nervous personality and ear notches. After two moons of training he realized that this was not normal and tried to run and tell the leader. That exact attempt in letting out the truth about Eagletalon was exactly how he got the long scar on his belly. He almost died from it. His mentor blamed it on a fox and nobody questioned the excuse. Coldpaw wasn't done there. He had to tell someone. He tried again and that was when Eagletalon explained. He told Coldpaw that he was getting revenge on Ravencall (his mother) for choosing Sunfeather (his father) over him. Then by pure luck, just before Eagletalon could kill his own apprentice a patrol caught him and prevented him from ending Coldrain's life. They banished him from the Clan when the truth was let out, and chasing him far from the Clan's territory. By then Coldpaw was ready for his warrior ceremony. A moon after his ceremony Coldrain met Cedarbush, the only cat in the Clan who could calm his nerves and allowed him to put his apprenticeship in the past. They later became mates even though Coldrain is still a bit of a nervous wreck, he lives happily by Cedarbush's side to this day.
Definitely complex, longer is a good thing, but I feel it is to similar to Ravenpaw's story and Eagletalon reminds of Tigerstar and Ashfur if they were mashed together. At least Coldrain got a happy ending and I like the names. The personality makes more sense now.
Death: He is still alive but he will die at 52 moons of age in a war between TorrentClan and DawnClan (ThunderClan and ShadowClan if canon) and is killed by a she-cat named Quaildusk
Okay, so he dies a little young with a warrior's death. I love the name Quaildusk.
Overall: the backstory is a little cliché and unoriginal but very good overall. Everything seems to correspond so that good.