TRex, I gather the way you like to play Chihuahua is to find as many of the common words as possible, while avoiding all rare words. Hence your decision not to play woolly when you thought it would be classed as rare. Jacki, I get the impression you play the puzzle this way too. In effect this way of playing requires you to predict whether each word you think of will be classed as common or rare. Given the rough and ready way this classification was set up - as I've described somewhere - you are setting yourselves quite a task.
I've said before that I have no problem with people playing Chihuahua however they wish. Still, the puzzle is not designed to be played in this way. This is obvious from the "How to play" section right under the puzzle on the main page: "Make as many words as you can with the letters given..." And from the first sentence on the Help pages: "Use the letters shown to make as many words as you can." (Emphasis added.) When I play, if I think something is a word, I'll play it.
So, in refining the word list, I'm not inclined to aim for predictability if I think that one variant of a word is actually more commonly used and known than another.
In this case, we currently have wooly, woolier and wooliest as rare words and the double-L versions of these words as common words. My spell checker queries the single-L words, but let's look further. The online Oxford identifies wooly as a US variant spelling, but the two main US-published dictionaries, Merriam-Webster and American Heritage both have woolly as the main entry. M-W says, "variants: or less commonly wooly".
Looking at usage frequency, woolly is about 3 times as common in US texts in both the News on the Web corpus and the Corpus of Contemporary American Usage. (A surprising number of the occurrences of wooly are in references to "Wooly Bully", the 1964 song by Sam the Sham and the Pharaohs.) In British news articles woolly outnumbers wooly by more than 10 to 1. The Google Ngrams viewer shows woolly used vastly more often than wooly in both American English and British English.
I feel the current classifications are probably correct.