First of all to the comment by Follow your HEART.
Drizzle is a verb for light rain, Drizzly is the adjective, so in this case, use drizzly, because you enjoy drizzly days.
"The". Both can make sense in this case, but they have different strengths of "most" due to the stress on the word.
Putting "the" into the sentence increases the stress and intonation on the word "most", so it becomes a superlative and tells us you enjoy drizzly days over all other days.
Without "the", the sentence can still make sense, but only when you are answering a question with 2 choices (e.g. Do you prefer rainy or drizzly days most? You could answer with both 1. and 2.).
It is a very complex use, but I would recommend always including "the", because "the" is only left out in special situations, and even then, you can use "the". So to be safe, always use "the".