Is using a distinct pitch or tone in your voice for your hint legal in Codenames? I.e., "colddd" to link "blanket" and "Arctic"

Codenames is not a hard game to break. All the clue giver needs to do is not have a full control of their facial expressions, and things are spoiled. Just reaching for a red or blue card too early can break things.

Even if players don't have facial expressions there are other ways to pass information completely legally that is not in the spirit of the game. Let's say you have your team read out loud all the words, and give your clue when they say your word. Legal, but I would not keep playing with that group.

Sp now we come to your question. This is just another way to leak information aside from the very analytical Codenames rule set. I would say don't do it. The spirit of the game is very explicit. You state one word, and it is a specific word. In fact the game tells you to spell the word if the specific word is not clear. It also tells you not to use words for anything but their meaning in relation to other words. Don't give card locations, or something about the spelling of the word. I am pretty sure the designer did not want you to use noises or intonations either.

The way I read the rules when you guess a word, you should be able to explain why that word, not the noise, not other hints, lead you to pick it. If you can't you are not following the spirit of the game.

My interpretation of the (default) rules on homonyms is that the way you pronounce the word may be variously "colored", while staying within limits of at least occasional pronunciation of the word in the given language, and if you are requested to spell the word as per the rules on homonyms, you should spell it "c-o-l-d". If you have to repeat the clue upon request, you should be trying to produce the same sound every time, as if it was the only way you can pronounce that word.

Dictionaries cover even standard pronunciations, not just the standard written forms of words, but dictionaries can hardly be taken as exhaustive. It's better to consult with the opposing spymaster beforehand.

It looks like this could reasonably be considered to violate either the rule that the word must be in English ("colddd" is not in any dictionary of the English language) or the rule that your clue must be "only one word" without any additional hints.

That is: it's not "only one English word without any additional hints". With the extra information you're attempting to convey in the manner you say the word, you're either turning it into the non-English word "colddd", or you're adding additional hints to the word "cold".

As some of the comments note, though, you're not really getting any extra benefit from trying to add the hint in this case, so you should probably just stick to "cold, 2" in the first place (it still means "cold"), but that's just kicking the can down the road.

If the way you say a word matters, then that probably constitutes an "additional hint".

Consider a different example: clueing the two words "opera" and "monkey" by singing "gorilla" in opera form like "Figaro". One word, sure, but with additional hints added in the way you pronounce it.

But, as always, it's up to your group how much you want to hew to the rules, as per the "golden rule" of Codenames:

If the opposing spymaster allows it, the clue is valid. If you aren't sure, ask your opponent.

I gave a similar answer to a different question here But this is a different question with almost the same answer.

The rules here say

DON'T BE TOO STRICT

So if the word is a legal clue then there is nothing in the rule to say you can't use a certain voice. I guess the balance is you couldn't use Western Film accent to say "Paris" to give a clue for "Cowboy" and "France".

Also its worth looking at the rules for Homonyms which say (emphasis mine).

Some people prefer to allow a more liberal use of homonyms. You can allow knight to be a clue for night-related things if that makes the game more fun for you.

You can apply that rule to making sounds with you clues. Would saying "colddd" make the make more fun for your group? If so then yes it would be fine.

In general if you're not sure if a clue is legal ask your self, Do the rules specially say you're not allowed to do it? If the answer is no, and your group are having fun then the clue is almost certainly fine.