Is verb+点儿 an adverb?
点儿 actually is not attached to the verb in this case and thus is not an adverb. Instead, 点 is being used as a measure word for the noun 衣服. The 儿 is the result of erhua (儿化) on 点, which is common in northern China.

一点 or 一点儿 is used as a measure to indicate "some" or "a little". When the count for a measure is one (一), it is often optional and can be dropped. Also note that when the noun is understood from context, it can also be dropped, so your sentence could also simply end up becoming 你要多穿点儿. This may end up making it look like 点儿 is modifying the verb, even though that's not the case; it's modifying an implicit noun that had been dropped.

It's true that this phenomenon of word dropping can often make sentences harder to analyze for Chinese learners, but learning when certain parts of sentences can be optional will help your understanding of the language.