Breakdown of Мама повязывает тёплый платок перед выходом из дома.
Questions & Answers about Мама повязывает тёплый платок перед выходом из дома.
Мама is the subject of the sentence, so it is in the nominative case. Even though it ends in -а, it is a normal feminine noun of the first declension.
Also, Russian has no articles, so Мама can mean Mom, Mother, or just the mother, depending on context.
The verb повязывать / повязать is used for tying something on, especially something like a scarf, kerchief, or bandage.
Here it suggests that she is putting on the scarf by tying it. That is more specific than a general verb like надевать, which means to put on clothing/accessories more broadly.
So повязывает платок is natural because a платок is often something you tie.