Do you know why we say 'many clothes'? Because it's right! 'Much' clothes is WRONG. We can only use 'much' with singular nouns - for example, much time, much money, much water. 'Clothes' is obviously a plural noun. Just look at the 's' at the end of it! Just look at the plural verb (are) which you used in your sample sentence! With a plural noun and a plural verb, you can only use 'many'. It should be "There are too many clothes in the dresser." Clothes is not - grammatically - an uncountable noun. Uncountable nouns are singular - 'clothes' is plural, so it cannot be an uncountable noun in a grammatical sense. The term 'uncountable' is very misleading. In fact, 'clothes' is a plural noun with no singular form. There's no such thing as a 'clothe'. It's the same as 'scissors' and 'pants' - these are plural words, even though there's no such thing as 'a scissor' or 'a pant'. I hope that helps.

I would never say "too much clothes" but I would say "too much clothing."

"There are too many clothes in the dresser." That's the correct sentence. No need to analyse it any further.

I would use too many clothes or so many clothes. I don't know if it grammatically correct though.