These things you will need all year:

Sun glasses for sitting out on terazas.
Beach wear - If you go on an excursion to the beach.
Sun tan lotion for sitting in the sun.
Comfortable walking shoes.
High heels are no good in Granada.

Note: Granada is 670 metres high so temperatures are lower at night
It has a dry climate so 30C is very pleasant.
(30C in London is horrendous, the comfortableness of temperature depends a lot on the humidity)

Here are some ideas according to months.

January:
Can get to just below freezing at night.
Many sunny days with blue skies and 22C at midday.
Warm clothes.
Heavy jersey and coat.

February:
Can get to just below freezing at night.
The coldest time is around the 14th Feb
Many sunny days with blue skies and 22C at midday.
Warm clothes.
Heavy jersey and coat.


March:
Can get to just around 5C at night.
Many sunny days with blue skies and 24C at midday.
Warm clothes.
Heavy jersey and coat.

April:
Can get to around 8C at night.
It can rain a lot in April especially at Easter.
Many sunny days with blue skies and 26C at midday.
Warm clothes.
Jersey and coat.

May:
Can get to just around 12C at night.
There is often a lot of rain at the start of May.
Many sunny days with blue skies and 30C at midday.
Light jersey.
Shirts and T shirts

June:
Not cold at any time
Almost all  sunny days with blue skies and 32C at midday.
Shirts and T shirts

July:
Warm at night.
Maybe a sheet or nothing on the bed.
Mosquito machines need to be used.
All days are hot some days are too hot.
After 9pm the temperature is almost always pleasant unless there is a weird wind from the Sahara.
Almost all  sunny days with blue skies and 36C at midday.
Shirts, T shirts, shorts, open sandals, very light clothes (cotton if possible)
The end of July can be very hot.

August:
The same as July but by about 16th August the really very hot days are over.
There are often summer storms with torrential rain.

September:
The best time to come to Granada by climate.
Warm at night.
Maybe a sheet or a light blanket on the bed.
Air conditioning completely not necesary
Many sunny days with blue skies and 28C at midday.
Light jersey.
Shirts and T shirts

October:
Weather starts to get cooler around the 10th October.
A light blanket on the bed.
Many sunny days with blue skies and 26C at midday.
Jersey.
Shirts and T shirts
Heavier Jersey towards the end of October.

November:
First signs of cooler weather.
Many days in November have beautiful blue skies lasting all day long
and the sun is not to hot to sit in.
A  blanket on the bed.
Domestic heating starts to be required around the 10th of November.
Many sunny days with blue skies and 24C at midday.
Jersey.
Shirts and T shirts
Heavier Jersey for nightime.

December:
Can get to around 2C at night.
Many sunny days with blue skies and 22C at midday.
Warm clothes.
Heavy jersey and coat.

Further reading:
What to Bring on a trip to Granada.
http://granadainfo.com/bring_stuff.htm