Even now in Madrid in October, there is a chill in the air most nights. According to the BBC website forecast earlier this week the minimum temperature was going to be -6C on Friday (they have adjusted this to -4C). So you can believe that later on in the winter it gets cold here - in fact there are ski-resorts only around 40 miles or so from here.
Apologies for those not bought up with the Centrigrade scale. My guess is that -4C relates to about 18 F, but you will have to check this out as my guess is very approximate.
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An English Bookseller in Madrid