Familiars can come through in any form. They are souls that we share kinship with that aid us along the way. Animal familiars are come and go throughout our lives.
My dog is a goofy familiar. I can't keep him away when I'm practicing magick or AP. And if I try to lock him out of the room he cries and scratches at the door. When I do let him in. He sleeps in my circle. But sometimes he gets mischevious and tries to dig a pretend hole next to me or knocks over my water dish! He's a misfit, but I love him, and he and I understand each other well. But cats are so much nicer. I had a cat familiar who would sit, as if guarding right outside my circle, and watch me while I practiced. Like you, he followed me home one cold snowy night. And my dog showed up at my front door literally! I opened it up and there he was, skinny and neglected. We bonded immediately.
Yes, I do believe this cat is a familiar soul to you. And you will find many more. But you must always take care to show attention to the ones that come into your life, as they show themselves.
Some don't always stay though. So don't be too upset if this is just a fleeting time.
One night on Yule, I was very depressed. It was the only Yule I spent alone in my entire life. I decided to take a walk, despite the fact that it was bitter cold outside, I felt drawn to just roaming my neighborhood. Sitting outside of a house was an orange and white cat. I said "hi" to him and continued walking. But he began to meow, and wouldn't stop, he chased after me and rolled over directly in my path! I'm not one to pet random animals so I bent down a bit and cooed to him. He got up and started rubbing on me. I offered my hand out and he began petting himself with my hand. I laughed and tried to continue walking again, but he followed me and laid in my path again! I ended up spending 30min with this cat and realized that my sadness was lifted. He finally just got up and walked away. And I thanked him, realizing that he had done what he intended to. I went home straight away and went to sleep, feeling a lot better about my not so lonely Yule. I tried walking that same path to reunite with my cat friend, but never saw him again.