because o σκούφος is male? And the sentence starts with "το μικρό" indicating the required answer needs to be of neuter gender? Not an expert, but that is my best guess.
Not exactly. We are talking two different pieces of clothing. Σκούφος is (as Troll1995 said) a winter cap, for the head, while κασκόλ is a scarf. :P (But yes, someone could exclude the word σκούφος for the gender alone.)
I was given this question as a drop-down box, with the sentence "το μικρό ------ μου" as the only clue. Am I right in thinking that gender is the only way to determine the correct word, in this type of question? Are there other clues to look for?
In this particular question, you can only determine the correct answer by gender. Ο σκούφος is masculine, η φράουλα is feminine so only κασκόλ can be correct.
It derives from French "cache-col" being a compound consisting of "cacher" (to hide, to cache) and "col" = neck.
So literally it translates as something like "neck hider".