I remember when my mother and I took a walk (for homeschool P.E. credit) around the block in -20 weather. It was windy too!
A little cat was outside. This cat wanted to be inside with us. She followed us for a mile. She found our sliding door and shivered dramatically outside until we finally let her in.
Mom was resolute. It took her more than a day. But she lived with us for years. She looked vaguely Asian, so we called her Chang.
Stray cats can be very pursuasive: