What's the word to decribe someone's voice when they talk with their nose closed?

Hyponasal (adjective) or hyponasality (noun) seems to be the word for this, so hyponasally would be a possible adverb. Wikipedia defines it thus:

Hyponasal speech, denasalization or rhinolalia clausa is a lack of appropriate nasal airflow during speech,[1] such as when a person has nasal congestion.

The American Speech-Language-Hearing Association is more technical:

Hyponasality—occurs when there is not enough nasal resonance on nasal sounds due to a blockage in the nasopharynx or nasal cavity.

(Apparently the term "nasal speech" can be used to refer to people who have too much or too little air through their nose, but because of the ambiguity I'd avoid it in the latter sense. Here's a letter from the European Journal of Human Genetics noting that ambiguity.)

I think you might have your adjectives round the wrong way.... someone who talks as if they have a clothes peg on their nose talks 'nasally'.

Nasally is an adjective used to describe the way one's voice sounds with a cold, or with a stuffy nose.

The opposite of nasally, would be clear, normal speech.

Nasalization or When to speak through your nose. Like many other languages, Gaelic has nasalized vowels. In linguist-speak that means that you lower your velum while making the vowel sound. In other words, instead of air passing just through your mouth, some air also escapes through your nose.

It is hyponasal voice. It's the same voice as you are speaking by pinching your nose, generally occurs when something stuffed. It's common in cold with running nose.